{"query": "Powers of two — the binary ladder", "count": 20, "results": [{"id": "card_n_a84694b9ae04", "title": "Powers of two — the binary ladder", "shelf": "science", "surface": "secular", "snippet": "The numbers a machine counts by, sealed: 2^10 = 1024 (the binary 'kilo'), 2^16 = 65,536\n(a 16-bit word's range), 2^30 = 1,073,741,824 (one GiB): https://narrowhighway.com/s/19df661045aef6fa486083cfbff"}, {"id": "card_c_1219a284fc2a", "title": "Quartz at 32,768 Hz — a power of two on the  ↔ Powers of two — the binary ladder", "shelf": "connections", "surface": null, "snippet": "run the signal through fifteen binary flip-flops, each halving the frequency, and the last ticks once per second... Time, on the wrist, is counted in powers of two.  — a concord the card itself states"}, {"id": "card_src_oeis_a002572", "title": "A002572 — Number of partitions of 1 into n powers of 1/2; or (according to one definition of \"binary\") the number of binary rooted trees.", "shelf": "oeis", "surface": "secular", "snippet": "Number of partitions of 1 into n powers of 1/2; or (according to one definition of \"binary\") the number of binary rooted trees.  First terms: 1, 1, 1, 2, 3, 5, 9, 16, 28, 50, 89, 159, 285, 510, 914, 1"}, {"id": "card_c_cfe6ced7e25d", "title": "Toki Pona — a whole language from 120 words ↔ Powers of two — the binary ladder", "shelf": "connections", "surface": null, "snippet": "a tiny alphabet, richly combined, spells everything — the design reality keeps choosing (DNA, binary, the elements, words)  — a concord the card itself states; mined + verified."}, {"id": "card_src_oeis_a000120", "title": "A000120 — Ones-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).", "shelf": "oeis", "surface": "secular", "snippet": "Ones-counting sequence: number of 1's in binary expansion of n (or the binary weight of n).  First terms: 0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4, 1, 2, 2, 3, 2, 3, 3, 4."}, {"id": "card_src_word_ladder_back", "title": "ladder-back", "shelf": "dictionary", "surface": "secular", "snippet": "ladder-back: (noun) a chair with a ladder-back — syn: ladder-back chair · (noun) the backrest of a chair that consists of two uprights with connecting slats"}, {"id": "card_src_oeis_a000961", "title": "A000961 — Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).", "shelf": "oeis", "surface": "secular", "snippet": "Powers of primes. Alternatively, 1 and the prime powers (p^k, p prime, k >= 1).  First terms: 1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49."}, {"id": "card_src_word_binary_operation", "title": "binary operation", "shelf": "dictionary", "surface": "secular", "snippet": "binary operation: (noun) an operation that follows the rules of Boolean algebra; each operand and the result take one of two values — syn: boolean operation, binary arithmetic operation"}, {"id": "card_src_word_binary_arithmetic_operation", "title": "binary arithmetic operation", "shelf": "dictionary", "surface": "secular", "snippet": "binary arithmetic operation: (noun) an operation that follows the rules of Boolean algebra; each operand and the result take one of two values — syn: boolean operation, binary operation"}, {"id": "card_src_oeis_a003824", "title": "A003824 — Numbers that are the sum of two 4th powers in more than one way (primitive solutions).", "shelf": "oeis", "surface": "secular", "snippet": "Numbers that are the sum of two 4th powers in more than one way (primitive solutions).  First terms: 635318657, 3262811042, 8657437697, 68899596497, 86409838577, 160961094577, 2094447251857, 423152522"}, {"id": "card_n_3f25971a39e2", "title": "Easton: Chronicles, Books of", "shelf": "dictionary", "surface": "secular", "snippet": "The two books were originally one. They bore the title in the Massoretic Hebrew Dibre hayyamim, i.e., “Acts of the Days.” This title was rendered by Jerome in his Latin version “Chronicon,” and hence "}, {"id": "card_src_oeis_a000003", "title": "A000003 — Number of classes of primitive positive definite binary quadratic forms of discriminant D = -4n; or equivalently the class number of the quadratic order of discriminant D", "shelf": "oeis", "surface": "secular", "snippet": "Number of classes of primitive positive definite binary quadratic forms of discriminant D = -4n; or equivalently the class number of the quadratic order of discriminant D = -4n.  First terms: 1, 1, 1,"}, {"id": "card_n_9d42516b140c", "title": "Quartz at 32,768 Hz — a power of two on the wrist", "shelf": "science", "surface": "secular", "snippet": "Every quartz watch cuts a tuning fork to hum at exactly 2^15 = 32,768 Hz, sealed, and\n32768 / 2^15 = 1: run the signal through fifteen binary flip-flops, each halving the frequency,\nand the last ticks"}, {"id": "card_src_oeis_a002474", "title": "A002474 — Denominators of coefficients of odd powers of x of the expansion of Bessel function J_1(x).", "shelf": "oeis", "surface": "secular", "snippet": "Denominators of coefficients of odd powers of x of the expansion of Bessel function J_1(x).  First terms: 2, 16, 384, 18432, 1474560, 176947200, 29727129600, 6658877030400, 1917756584755200, 690392370"}, {"id": "card_n_ac7a1b4d5c0d", "title": "Easton: Kings, The Books of", "shelf": "dictionary", "surface": "secular", "snippet": "The two books of Kings formed originally but one book in the Hebrew Scriptures. The present division into two books was first made by the LXX., which now, with the Vulgate, numbers them as the third a"}, {"id": "card_src_oeis_a001160", "title": "A001160 — sigma_5(n), the sum of the 5th powers of the divisors of n.", "shelf": "oeis", "surface": "secular", "snippet": "sigma_5(n), the sum of the 5th powers of the divisors of n.  First terms: 1, 33, 244, 1057, 3126, 8052, 16808, 33825, 59293, 103158, 161052, 257908, 371294, 554664, 762744, 1082401, 1419858, 1956669, "}, {"id": "card_n_5a0d951f0365", "title": "Easton: Ezra, Book of", "shelf": "dictionary", "surface": "secular", "snippet": "This book is the record of events occurring at the close of the Babylonian exile. It was at one time included in Nehemiah, the Jews regarding them as one volume. The two are still distinguished in the"}, {"id": "card_n_734bcd21be45", "title": "Easton: Joshua, The Book of", "shelf": "dictionary", "surface": "secular", "snippet": "Contains a history of the Israelites from the death of Moses to that of Joshua. It consists of three parts: (1.) The history of the conquest of the land (1-12). (2.) The allotment of the land to the d"}, {"id": "card_src_oeis_a000358", "title": "A000358 — Number of binary necklaces of length n with no subsequence 00, excluding the necklace \"0\".", "shelf": "oeis", "surface": "secular", "snippet": "Number of binary necklaces of length n with no subsequence 00, excluding the necklace \"0\".  First terms: 1, 2, 2, 3, 3, 5, 5, 8, 10, 15, 19, 31, 41, 64, 94, 143, 211, 329, 493, 766, 1170, 1811, 2787, "}, {"id": "card_n_0667b6bec0dd", "title": "Easton: Jeroboam", "shelf": "dictionary", "surface": "secular", "snippet": "Increase of the people. (1.) The son of Nebat (1 Kings 11:26-39), “an Ephrathite,” the first king of the ten tribes, over whom he reigned twenty-two years (B.C. 976-945). He was the son of a widow of "}]}