cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A334836 a(n) = A334769(k) where k is the first position of n in A334796.

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%I A334836 #7 May 20 2020 17:57:29
%S A334836 151,543,10707,33151,345283,2213663,33629695,134297599,1109207903,
%T A334836 8657682303,73283989519
%N A334836 a(n) = A334769(k) where k is the first position of n in A334796.
%C A334836 This sequence indexes the smallest number m = A334769(k) that, when expressed in binary b(k), generates a rotationally symmetrical XOR-triangle (RST) that features a central zero-triangle (CZT) with frame width n.
%C A334836 A "frame width" is the number of iterations j required to generate the first run of zeros in a CZT of an RST.
%C A334836 Let L = A070939(m) for m in A334769. For RSTs, j > 1, since a solid run of L 1s given a recursive XOR function applied to each pair of adjacent bits, would give rise to a solid run of (L - 1) zeros in the next iteration, and every iteration thereafter consists of zeros. Therefore m = (2(L - 1) - 1) is not rotationally symmetrical except when L = 1.
%C A334836 Sequence A334556 lists numbers m that produce RSTs; A334769 those RSTs that feature CZTs. Sequence A334796 renders the frame widths j for numbers in A334769.
%C A334836 For n = 7, A070939(a(n)) > 3(7) + 1 = 22, but is likely much larger, given a(6). a(7) is likely a number with more than 40 bits.
%H A334836 Michael De Vlieger, <a href="/A334836/a334836.png">Diagram montage</a> showing XOR-triangles of each a(n) for 2 <= n <= 12.
%H A334836 Michael De Vlieger, <a href="/A334836/a334836.txt">Aspects of XOR-triangles T(a(n))</a>
%e A334836 a(2) = 151; Rotationally symmetrical XOR-triangle generated by 151, replacing 0s with "." for clarity, showing 2 bits to reach the central zero triangle of side length s = 2:
%e A334836   1 . . 1 . 1 1 1
%e A334836    1 . 1 1 1 . .
%e A334836     1 1 . . 1 .
%e A334836      . 1 . 1 1
%e A334836       1 1 1 .
%e A334836        . . 1
%e A334836         . 1
%e A334836          1
%e A334836 a(3) = 543; RST generated by 543, showing 3 bits to reach the CZT of side length s = 1 = A334770(3):
%e A334836   1 . . . . 1 1 1 1 1
%e A334836    1 . . . 1 . . . .
%e A334836     1 . . 1 1 . . .
%e A334836      1 . 1 . 1 . .
%e A334836       1 1 1 1 1 .
%e A334836        . . . . 1
%e A334836         . . . 1
%e A334836          . . 1
%e A334836           . 1
%e A334836            1
%Y A334836 Cf. A016777, A070939, A334556, A334769, A334796.
%K A334836 nonn,more
%O A334836 2,1
%A A334836 _Michael De Vlieger_, May 13 2020