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 A295653 #8 Nov 27 2017 12:46:09 %S A295653 0,0,1,0,2,2,0,1,4,3,0,4,4,6,4,0,1,8,5,8,5,0,2,2,12,8,10,6,0,1,8,3,16, %T A295653 9,12,7,0,8,8,10,8,20,12,14,8,0,1,16,9,16,9,24,13,16,9,0,2,2,24,16,18, %U A295653 10,28,16,18,10,0,1,4,3,32,17,24,11,32,17,20 %N A295653 Square array T(n, k), n >= 0, k >= 0, read by antidiagonals upwards: T(n, k) = the (k+1)-th nonnegative number m such that n AND m = 0 (where AND denotes the bitwise AND operator). %C A295653 This sequence has similarities with A126572: here we check for common bits in binary representations, there for common primes in prime factorizations. %C A295653 For any n >= 0 and k >= 0: %C A295653 - T(0, k) = k, %C A295653 - T(1, k) = 2*k, %C A295653 - T(2, k) = A042948(k), %C A295653 - T(3, k) = 4*k, %C A295653 - T(4, k) = A047476(k), %C A295653 - T(5, k) = A047467(k), %C A295653 - T(2^n - 1, k) = 2^n * k, %C A295653 - T(n, 0) = 0, %C A295653 - T(n, 1) = A006519(n+1), %C A295653 - T(n, k + 2^A080791(n)) = T(n, k) + 2^A029837(n+1) (i.e. each row is linear), %C A295653 - A000120(T(n, k)) = A000120(k). %F A295653 For any n >= 0 and k >= 0: %F A295653 - T(0, k) = k, %F A295653 - T(2*n + 1, k) = 2*T(n, k), %F A295653 - T(2*n, 2*k) = 2*T(n, k), %F A295653 - T(2*n, 2*k + 1) = 2*T(n, k) + 1. %F A295653 For any n >= 0, T(n, k) ~ 2^A000120(n) * k as k tends to infinity. %e A295653 Square array begins: %e A295653 n\k 0 1 2 3 4 5 6 7 8 9 ... %e A295653 0: 0 1 2 3 4 5 6 7 8 9 ... %e A295653 1: 0 2 4 6 8 10 12 14 16 18 ... %e A295653 2: 0 1 4 5 8 9 12 13 16 17 ... %e A295653 3: 0 4 8 12 16 20 24 28 32 36 ... %e A295653 4: 0 1 2 3 8 9 10 11 16 17 ... %e A295653 5: 0 2 8 10 16 18 24 26 32 34 ... %e A295653 6: 0 1 8 9 16 17 24 25 32 33 ... %e A295653 7: 0 8 16 24 32 40 48 56 64 72 ... %e A295653 8: 0 1 2 3 4 5 6 7 16 17 ... %e A295653 9: 0 2 4 6 16 18 20 22 32 34 ... %o A295653 (PARI) T(n,k) = if (n==0, k, n%2, 2*T(n\2,k), 2*T(n\2,k\2) + (k%2)) %Y A295653 Cf. A000120, A006519, A029837, A042948, A047467, A047476, A080791, A126572. %K A295653 nonn,tabl,base %O A295653 0,5 %A A295653 _Rémy Sigrist_, Nov 25 2017