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 A342700 #12 Jan 10 2024 16:32:32 %S A342700 0,0,2,0,7,0,0,0,15,6,10,0,3,0,0,0,31,14,30,12,23,4,16,0,7,6,2,0,3,0, %T A342700 0,0,63,30,62,28,63,28,56,24,47,14,42,8,35,0,32,0,15,14,14,12,7,4,0,0, %U A342700 7,6,2,0,3,0,0,0,127,62,126,60,127,60,120,56,127,62 %N A342700 For any number n with binary expansion (b(1), b(2), ..., b(k)), the binary expansion of a(n) is (1-floor((b(k)+b(1)+b(2))/2), 1-floor((b(1)+b(2)+b(3))/2), ..., 1-floor((b(k-1)+b(k)+b(1))/2)). %C A342700 This sequence is a variant of A342698; here the value of the k-th bit of a(n) is the less frequent value in the bit triple centered around the k-th bit of n. %H A342700 Rémy Sigrist, <a href="/A342700/b342700.txt">Table of n, a(n) for n = 0..8191</a> %H A342700 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a> %F A342700 a(n) + A342698(n) = A003817(n). %F A342700 a(n) = n iff n belongs to A020988. %e A342700 The first terms, in decimal and in binary, are: %e A342700 n a(n) bin(n) bin(a(n)) %e A342700 -- ---- ------ --------- %e A342700 0 0 0 0 %e A342700 1 0 1 0 %e A342700 2 2 10 10 %e A342700 3 0 11 0 %e A342700 4 7 100 111 %e A342700 5 0 101 0 %e A342700 6 0 110 0 %e A342700 7 0 111 0 %e A342700 8 15 1000 1111 %e A342700 9 6 1001 110 %e A342700 10 10 1010 1010 %e A342700 11 0 1011 0 %e A342700 12 3 1100 11 %e A342700 13 0 1101 0 %e A342700 14 0 1110 0 %e A342700 15 0 1111 0 %o A342700 (PARI) a(n) = my (w=#binary(n)); sum(k=0, w-1, ((bittest(n, (k-1)%w)+bittest(n, k%w)+bittest(n, (k+1)%w))<=1) * 2^k) %Y A342700 Cf. A003817, A020988 (fixed points), A342698. %K A342700 nonn,base %O A342700 0,3 %A A342700 _Rémy Sigrist_, Mar 18 2021