A320263 - OEIS

%I #13 Oct 10 2018 12:43:31

%S 1,4,3,8,17,12,7,16,33,68,35,24,49,28,15,32,65,132,67,136,273,140,71,

%T 48,97,196,99,56,113,60,31,64,129,260,131,264,529,268,135,272,545,

%U 1092,547,280,561,284,143,96,193,388,195,392,785,396,199,112,225,452,227

%N 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.

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

%H Chai Wah Wu, <a href="/A320263/b320263.txt">Table of n, a(n) for n = 1..10000</a>

%H Chai Wah Wu, <a href="https://arxiv.org/abs/1810.02293">Record values in appending and prepending bitstrings to runs of binary digits</a>, arXiv:1810.02293 [math.NT], 2018.

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

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

%o (Python)

%o from re import split

%o def A320263(n):

%o     return int(''.join('0'+d for d in split('(0+)|(1+)',bin(n)[2:]) if d != '' and d != None),2)

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

%K nonn,base

%O 1,2

%A _Chai Wah Wu_, Oct 08 2018