A129600 -id:A129600 - cp's OEIS frontend

A129602 In the binary expansion of n replace each run of k 0's (or 1's) with 2k-1 0's (or 1's), except in the most significant run where we double the number of 0's (or 1's).

0, 3, 6, 15, 24, 13, 30, 63, 96, 49, 26, 55, 120, 61, 126, 255, 384, 193, 98, 199, 104, 53, 110, 223, 480, 241, 122, 247, 504, 253, 510, 1023, 1536, 769, 386, 775, 392, 197, 398, 799, 416, 209, 106, 215, 440, 221, 446, 895, 1920, 961, 482, 967, 488, 245, 494

Offset: 0

Antti Karttunen, May 01 2007

			a(1) = 3, as 1 is 1 in binary and doubling the number of 1's (in the only run) gives binary 11, 3 in decimal. a(9) = 49, as 9 is 1001 in binary and replacing the most significant run '1' with '11' and the center run '00' with '000' and the least significant run '1' with '1', we get 110001 in binary, 49 in decimal.

Central diagonal of array A129600, a(n) = A129600bi(n, n). Cf. A129594. For n > 0, a(n) = A004760(A129603(n)+1).

Edited definition. - N. J. A. Sloane, Dec 20 2023

A129601 Table T(i,j): T(0,0), T(1,0), T(1,1), T(2,0), T(2,1), T(2,2), ... of binary runlength encoded product of i and j.

Original entry on oeis.org

0, 1, 3, 2, 4, 6, 3, 7, 8, 15, 4, 8, 12, 16, 24, 5, 11, 9, 23, 19, 13, 6, 12, 14, 24, 28, 17, 30, 7, 15, 16, 31, 32, 47, 48, 63, 8, 16, 24, 32, 48, 39, 56, 64, 96, 9, 19, 17, 39, 35, 25, 33, 79, 71, 49, 10, 20, 22, 40, 44, 18, 46, 80, 88, 38, 26, 11, 23, 19, 47, 39, 27, 35, 95

Offset: 0

Antti Karttunen, May 01 2007

This is the upper triangular region of array A129600 (or equally, the lower triangular region, because A129600 is symmetric).

cp's OEIS Frontend

A129602 In the binary expansion of n replace each run of k 0's (or 1's) with 2k-1 0's (or 1's), except in the most significant run where we double the number of 0's (or 1's).

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A129601 Table T(i,j): T(0,0), T(1,0), T(1,1), T(2,0), T(2,1), T(2,2), ... of binary runlength encoded product of i and j.

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