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A044051 a(n) = (s(n)+1)/2, where s=A006995 (base-2 palindromes). 6

%I #17 Apr 13 2021 23:22:51

%S 1,2,3,4,5,8,9,11,14,16,17,23,26,32,33,37,43,47,50,54,60,64,65,77,83,

%T 95,98,110,116,128,129,137,149,157,163,171,183,191,194,202,214,222,

%U 228,236,248,256,257,281,293,317,323,347,359,383

%N a(n) = (s(n)+1)/2, where s=A006995 (base-2 palindromes).

%C A141707(a(n)) = 1. - _Reinhard Zumkeller_, Apr 20 2015

%H Reinhard Zumkeller, <a href="/A044051/b044051.txt">Table of n, a(n) for n = 1..10000</a>

%F Let n >= 3, m=floor(log_2(n)), p=floor((3*2^(m-1)-1)/n); then a(n) = 2^(2*m-2-p) + 1 + p*(1-(-1)^n)*2^(m-1) + (1/2)*Sum_{k=1..m-1-p} (floor((n - (3-p)*2^(m-1))/2^(m-1-k)) mod 2)*(2^k + 2^(2*m-1-p-k)). - _Hieronymus Fischer_, Feb 18 2012

%o (Haskell)

%o a044051 = (`div` 2) . (+ 1) . a006995 . (+ 1)

%o -- _Reinhard Zumkeller_, Apr 20 2015

%Y Cf. A006995, A141707.

%K nonn,base

%O 1,2

%A Melia Aldridge, ma38(AT)spruce.evansville.edu

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Last modified April 19 13:40 EDT 2024. Contains 371792 sequences. (Running on oeis4.)