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A334595 Binary interpretation of the right diagonal of the XOR-triangle with first row generated from the binary expansion of n.

%I A334595 #18 May 09 2020 00:59:35
%S A334595 1,1,2,1,6,3,4,1,14,4,11,2,13,7,8,1,30,11,20,7,24,13,18,3,28,9,22,5,
%T A334595 26,15,16,1,62,20,43,13,50,24,39,5,58,16,47,9,54,28,35,2,61,23,40,14,
%U A334595 49,27,36,6,57,19,44,10,53,31,32,1,126,43,84,24,103,50
%N A334595 Binary interpretation of the right diagonal of the XOR-triangle with first row generated from the binary expansion of n.
%C A334595 An XOR-triangle is an inverted 0-1 triangle formed by choosing a top row and having each entry in the subsequent rows be the XOR of the two values above it.
%C A334595 a(n) = n if and only if n is in A334556.
%C A334595 Conjecture: Records occur at 1 and at 2^n + 1.
%C A334595 Conjecture: a(n) = 1 if and only if n is a power of two.
%H A334595 Peter Kagey, <a href="/A334595/b334595.txt">Table of n, a(n) for n = 1..8191</a> (values less than 2^13)
%H A334595 MathOverflow user DSM, <a href="https://mathoverflow.net/q/359138/104733">Number triangle</a>
%H A334595 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%e A334595 For n = 19, the binary expansion of 19 is 10011_2, and the XOR-triangle with first row generated from the binary expansion of 19 is:
%e A334595   1 0 0 1 1
%e A334595    1 0 1 0
%e A334595     1 1 1
%e A334595      0 0
%e A334595       0
%e A334595 Reading the right side of the triangle starting from the upper-right corner gives 10100 which is the binary representation of 20 = a(19).
%o A334595 (PARI) a(n) = {my(b=binary(n), v=vector(#b)); v[#b] = b[#b]; for (n=1, #b-1, b = vector(#b-1, k, bitxor(b[k], b[k+1])); v[#b] = b[#b];); fromdigits(Vecrev(v), 2);} \\ _Michel Marcus_, May 08 2020
%Y A334595 Cf. A334556, A334591, A334592, A334593, A334594, A334596.
%K A334595 nonn,base,look
%O A334595 1,3
%A A334595 _Peter Kagey_, May 07 2020