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 A348624 a(n) = sum of row n of A348433 expressed as an irregular triangle. 1
 31, 21, 2555, 2805, 3315, 17391, 38893, 104857575, 59363, 2097120, 31713, 376809, 117440484, 18790481885, 197132241, 2885681109, 42991575, 4966055899, 13153337295, 3959422917, 120946279055305, 4191888080835, 3729543441416139, 321057395310519, 84662395338675, 294669116243901 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The binary expansion w of a(n) has an interesting appearance shown by the bitmap in links. We may divide w with length m into 3 parts: the most significant part includes all bits including the last 0 before the middle of the word, m/2, a central run of k 1's that includes all but the last 1 before a 0, and a least significant part that includes the last 1 in the central run of 1s and an assortment of 0's. For example, a(3) = 2555 -> 100.11111.1011, which we may partition as shown by "." so as to preserve the otherwise-leading 0 in the last part. The central run of 1s generally increases in length as n increases. LINKS Michael De Vlieger, Table of n, a(n) for n = 1..1540 Michael De Vlieger, Log log scatterplot of a(n) for n=1..120. Michael De Vlieger, Log log scatterplot of a(n) for n=1..3961. Michael De Vlieger, Big-endian bitmap of the binary expansion of a(n) for n=1..3961 showing 1s in black and 0s in white. EXAMPLE Table showing the first 5 rows of A348433 each having A348408(n) terms, and their sum a(n): n\k 1 2 3 4 5 6 7 8 9 a(n) binary(a(n)) -------------------------------------------------------------- 1: 1 2 4 8 16 -> 31 -> 11111 2: 7 14 -> 21 -> 10101 3: 5 10 20 40 80 160 320 640 1280 -> 2555 -> 100111111011 4: 11 22 44 88 176 352 704 1408 -> 2805 -> 101011110101 5: 13 26 52 104 208 416 832 1664 -> 3315 -> 110011110011 MATHEMATICA c[1] = m = q = 1; Most@ Reap[Do[If[IntegerQ[c[#]], Set[n, 2 m], Set[n, #]] &@ Total@ IntegerDigits[m]; If[m > n, Sow[q]; Set[q, n], q += n]; Set[c[n], 1]; m = n, 650]][[-1, -1]] (* Extract up to 3961 terms from bitmap: *) Block[{s = ImageData[ColorNegate@ Import["https://oeis.org/A348624/a348624_2.png"], "Bit"]}, Array[FromDigits[s[[#]], 2] &, 26]] (* Michael De Vlieger, Oct 26 2021 *) CROSSREFS Cf. A348408, A348433. Sequence in context: A040932 A298724 A299558 * A340744 A361315 A291471 Adjacent sequences: A348621 A348622 A348623 * A348625 A348626 A348627 KEYWORD nonn,base AUTHOR Michael De Vlieger, Oct 25 2021 STATUS approved

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Last modified September 13 17:14 EDT 2024. Contains 375910 sequences. (Running on oeis4.)