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 A334592 Number of zeros in XOR-triangle with first row generated from the binary expansion of n. 6
 0, 1, 1, 3, 2, 2, 3, 6, 4, 5, 3, 5, 3, 4, 6, 10, 7, 6, 7, 7, 8, 5, 6, 8, 7, 6, 5, 7, 6, 7, 10, 15, 11, 11, 9, 9, 9, 11, 9, 11, 9, 13, 9, 9, 7, 9, 9, 13, 9, 9, 11, 9, 9, 7, 9, 11, 9, 9, 9, 11, 9, 11, 15, 21, 16, 14, 15, 16, 13, 13, 12, 14, 11, 13, 12, 17, 12 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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. Conjecture: Records occur at powers of two. LINKS Peter Kagey, Table of n, a(n) for n = 1..8191 MathOverflow user DSM, Number triangle Index entries for sequences related to binary expansion of n FORMULA a(n) = A000217(A070939(n)) - A334593(n). EXAMPLE For n = 53, a(53) = 9 because 53 = 110101_2 in binary, and the corresponding XOR-triangle has 9 zeros: 1 1 0 1 0 1 0 1 1 1 1 1 0 0 0 1 0 0 1 0 1 MATHEMATICA Array[Count[Flatten@ NestWhileList[Map[BitXor @@ # &, Partition[#, 2, 1]] &, IntegerDigits[#, 2], Length@ # > 1 &], 0] &, 77] (* Michael De Vlieger, May 08 2020 *) PROG (PARI) a(n) = {my(b=binary(n), nb=#b-hammingweight(n)); for (n=1, #b-1, b = vector(#b-1, k, bitxor(b[k], b[k+1])); nb += #b-vecsum(b); ); nb; } \\ Michel Marcus, May 08 2020 CROSSREFS Cf. A000217, A070939. Cf. also A334556, A334591, A334593, A334594, A334595, A334596. Sequence in context: A335401 A324465 A361565 * A248756 A059942 A032450 Adjacent sequences: A334589 A334590 A334591 * A334593 A334594 A334595 KEYWORD nonn,base AUTHOR Peter Kagey, May 07 2020 STATUS approved

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Last modified December 11 01:45 EST 2023. Contains 367717 sequences. (Running on oeis4.)