A352750 a(n) = binary complement of b(n-1) AND b(n); a(1) = 1, where b(n) = A109812(n).
1, 0, 1, 0, 4, 2, 0, 5, 9, 0, 4, 1, 2, 0, 17, 24, 0, 6, 10, 0, 16, 8, 4, 2, 8, 16, 2, 0, 48, 41, 0, 20, 36, 0, 24, 36, 0, 18, 32, 8, 4, 32, 24, 0, 32, 16, 3, 8, 0, 39, 98, 0, 28, 96, 0, 28, 80, 0, 41, 81, 16, 8, 4, 2, 1, 4, 8, 1, 0, 48, 68, 0, 48, 64, 3, 32, 64
Offset: 1
Examples
Relation between a(n) and b(n) = A109812(n). The binary expansion of b(n) = b(n)_2 = A352575(n), showing zeros as "." to accentuate 1 bits: n b(n)_2 b(n) a(n) ---------------------- 1 1 1 1 2 1. 2 0 3 1.. 4 1 4 11 3 0 5 1... 8 4 6 1.1 5 2 7 1.1. 10 0 8 1.... 16 5 9 11. 6 9 10 1..1 9 0 11 1..1. 18 4 12 11.. 12 1 13 1...1 17 2 14 111. 14 0 15 1..... 32 17 16 111 7 24 ...
Links
- Rémy Sigrist, Table of n, a(n) for n = 1..10000
- Michael De Vlieger, Log-log scatterplot of a(n) for n = 1..2^16, substituting 1/2 for 0 so as to plot in blue, records labelled in red, fixed points shown in amber.
- Michael De Vlieger, Bitmap of a(n) for n = 1..2^10, where each term is shown vertically, with least significant bit at bottom, 12X vertical exaggeration. Black corresponds to 1 and white to 0.
- Michael De Vlieger, Bitmap of a(n) for n = 1..2^14, where each term is shown horizontally, with least significant bit at right, 256X horizontal exaggeration. Black corresponds to 1 and white to 0.
- Rémy Sigrist, PARI program
Programs
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Mathematica
c[_] = 0; a[1] = c[1] = 1; u = 2; {1}~Join~Reap[Do[k = u; While[Nand[c[k] == 0, BitAnd[a[i - 1], k] == 0], k++]; Set[{a[i], c[k]}, {k, i}]; Sow[FromDigits[IntegerDigits[BitOr[a[i - 1], a[i]], 2] /. {0 -> 1, 1 -> 0}, 2]]; If[k == u, While[c[u] > 0, u++]], {i, 2, 77}]][[-1, -1]] -
PARI
See Links section.
Formula
a(n) = 2^(1 + max(floor(log_2 i), floor(log_2 j))) - (i + j) - 1, with i = A109812(n-1) and j = A109812(n). - Michael De Vlieger, Apr 05 2022
Comments