A320263 Write n in binary, then modify each run of 0's and each run of 1's by prepending a 0. a(n) is the decimal equivalent of the result.

1, 4, 3, 8, 17, 12, 7, 16, 33, 68, 35, 24, 49, 28, 15, 32, 65, 132, 67, 136, 273, 140, 71, 48, 97, 196, 99, 56, 113, 60, 31, 64, 129, 260, 131, 264, 529, 268, 135, 272, 545, 1092, 547, 280, 561, 284, 143, 96, 193, 388, 195, 392, 785, 396, 199, 112, 225, 452, 227

Offset: 1

Author

Chai Wah Wu, Oct 08 2018

Keywords

• nonn
• base

Comments

A variation of A175046. Indices of record values are given by A319423.

Examples

			6 in binary is 110. Modify each run by prepending a 0 to get 01100, which is 12 in decimal. So a(6) = 12.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Chai Wah Wu, Record values in appending and prepending bitstrings to runs of binary digits, arXiv:1810.02293 [math.NT], 2018.

Crossrefs

Cf. A175046, A319423, A320037, A320038, A320039, A320261, A320262.

Programs

Python

from re import split
def A320263(n):
    return int(''.join('0'+d for d in split('(0+)|(1+)',bin(n)[2:]) if d != '' and d != None),2)

Formula

a(n) = A320262(n)/2.