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 A342698 #12 Jan 10 2024 16:31:22 %S A342698 0,1,1,3,0,7,7,7,0,9,5,15,12,15,15,15,0,17,1,19,8,27,15,31,24,25,29, %T A342698 31,28,31,31,31,0,33,1,35,0,35,7,39,16,49,21,55,28,63,31,63,48,49,49, %U A342698 51,56,59,63,63,56,57,61,63,60,63,63,63,0,65,1,67,0,67,7 %N A342698 For any number n with binary expansion (b(1), b(2), ..., b(k)), the binary expansion of a(n) is (floor((b(k)+b(1)+b(2))/2), floor((b(1)+b(2)+b(3))/2), ..., floor((b(k-1)+b(k)+b(1))/2)). %C A342698 This sequence is a variant of A342697; here we deal with bit triples in a "cyclic" binary representation of n. %H A342698 Rémy Sigrist, <a href="/A342698/b342698.txt">Table of n, a(n) for n = 0..8192</a> %H A342698 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a> %F A342698 a(n) + A342700(n) = A003817(n). %F A342698 a(n) = n iff n belongs to A342699. %e A342698 The first terms, in decimal and in binary, are: %e A342698 n a(n) bin(n) bin(a(n)) %e A342698 -- ---- ------ --------- %e A342698 0 0 0 0 %e A342698 1 1 1 1 %e A342698 2 1 10 1 %e A342698 3 3 11 11 %e A342698 4 0 100 0 %e A342698 5 7 101 111 %e A342698 6 7 110 111 %e A342698 7 7 111 111 %e A342698 8 0 1000 0 %e A342698 9 9 1001 1001 %e A342698 10 5 1010 101 %e A342698 11 15 1011 1111 %e A342698 12 12 1100 1100 %e A342698 13 15 1101 1111 %e A342698 14 15 1110 1111 %e A342698 15 15 1111 1111 %o A342698 (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))>=2) * 2^k) %Y A342698 Cf. A003817, A342697, A342699 (fixed points), A342700. %K A342698 nonn,base %O A342698 0,4 %A A342698 _Rémy Sigrist_, Mar 18 2021