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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.

%I A320263 #13 Oct 10 2018 12:43:31
%S A320263 1,4,3,8,17,12,7,16,33,68,35,24,49,28,15,32,65,132,67,136,273,140,71,
%T A320263 48,97,196,99,56,113,60,31,64,129,260,131,264,529,268,135,272,545,
%U A320263 1092,547,280,561,284,143,96,193,388,195,392,785,396,199,112,225,452,227
%N 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.
%C A320263 A variation of A175046. Indices of record values are given by A319423.
%H A320263 Chai Wah Wu, <a href="/A320263/b320263.txt">Table of n, a(n) for n = 1..10000</a>
%H A320263 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 A320263 a(n) = A320262(n)/2.
%e A320263 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 A320263 (Python)
%o A320263 from re import split
%o A320263 def A320263(n):
%o A320263     return int(''.join('0'+d for d in split('(0+)|(1+)',bin(n)[2:]) if d != '' and d != None),2)
%Y A320263 Cf. A175046, A319423, A320037, A320038, A320039, A320261, A320262.
%K A320263 nonn,base
%O A320263 1,2
%A A320263 _Chai Wah Wu_, Oct 08 2018