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A334836 a(n) = A334769(k) where k is the first position of n in A334796. 4
151, 543, 10707, 33151, 345283, 2213663, 33629695, 134297599, 1109207903, 8657682303, 73283989519 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,1
COMMENTS
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.
A "frame width" is the number of iterations j required to generate the first run of zeros in a CZT of an RST.
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.
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.
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.
LINKS
Michael De Vlieger, Diagram montage showing XOR-triangles of each a(n) for 2 <= n <= 12.
EXAMPLE
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:
1 . . 1 . 1 1 1
1 . 1 1 1 . .
1 1 . . 1 .
. 1 . 1 1
1 1 1 .
. . 1
. 1
1
a(3) = 543; RST generated by 543, showing 3 bits to reach the CZT of side length s = 1 = A334770(3):
1 . . . . 1 1 1 1 1
1 . . . 1 . . . .
1 . . 1 1 . . .
1 . 1 . 1 . .
1 1 1 1 1 .
. . . . 1
. . . 1
. . 1
. 1
1
CROSSREFS
Sequence in context: A164622 A176138 A139640 * A130870 A340436 A211555
KEYWORD
nonn,more
AUTHOR
Michael De Vlieger, May 13 2020
STATUS
approved

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Last modified June 14 08:50 EDT 2024. Contains 373393 sequences. (Running on oeis4.)