This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A374355 #11 Jul 09 2024 02:21:30
%S A374355 0,0,0,1,0,0,2,2,0,0,0,1,4,4,4,5,0,0,0,1,0,0,2,2,8,8,8,9,8,8,10,10,0,
%T A374355 0,0,1,0,0,2,2,0,0,0,1,4,4,4,5,16,16,16,17,16,16,18,18,16,16,16,17,20,
%U A374355 20,20,21,0,0,0,1,0,0,2,2,0,0,0,1,4,4,4,5,0
%N A374355 a(n) is the least fibbinary number f <= n such that n - f is also a fibbinary number whose binary expansion has no common 1's with that of f (where fibbinary numbers correspond to A003714).
%C A374355 To compute a(n): replace every other bit with zero (starting with the first bit) in each run of consecutive 1's in the binary expansion of n.
%H A374355 Rémy Sigrist, <a href="/A374355/b374355.txt">Table of n, a(n) for n = 0..8191</a>
%H A374355 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A374355 a(n) = A374354(n, 0).
%F A374355 a(n) = n - A374356(n).
%F A374355 a(n) >= 0 with equality iff n is a fibbinary number.
%e A374355 The first terms, in binary and in decimal, are:
%e A374355 n a(n) bin(n) bin(a(n))
%e A374355 -- ---- ------ ---------
%e A374355 0 0 0 0
%e A374355 1 0 1 0
%e A374355 2 0 10 0
%e A374355 3 1 11 1
%e A374355 4 0 100 0
%e A374355 5 0 101 0
%e A374355 6 2 110 10
%e A374355 7 2 111 10
%e A374355 8 0 1000 0
%e A374355 9 0 1001 0
%e A374355 10 0 1010 0
%e A374355 11 1 1011 1
%e A374355 12 4 1100 100
%e A374355 13 4 1101 100
%e A374355 14 4 1110 100
%e A374355 15 5 1111 101
%e A374355 16 0 10000 0
%o A374355 (PARI) a(n) = { my (v = 0, e, x, y, b); while (n, x = y = 0; e = valuation(n, 2); for (k = 0, oo, if (bittest(n, e+k), n -= b = 2^(e+k); [x, y] = [y + b, x], v += y; break;););); return (v); }
%Y A374355 Cf. A003714, A374354, A374356.
%K A374355 nonn,base
%O A374355 0,7
%A A374355 _Rémy Sigrist_, Jul 06 2024