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 A338884 #22 Nov 23 2020 01:47:23 %S A338884 1,1,1,2,1,1,2,1,1,2,1,3,2,1,1,2,2,1,2,1,1,2,1,2,2,1,2,2,1,1,2,2,1,2, %T A338884 1,1,2,3,1,2,1,3,2,1,2,3,2,1,2,1,1,2,1,1,2,1,2,2,2,2,3,2,1,2,1,4,2,1, %U A338884 1,2,3,3,2,1,1,2,2,1,2,3,1,2,1,2,3,1,2 %N A338884 The smallest number of bits which need to be appended to the binary representation of n to reach a prime greater than n. %C A338884 a(n) is also the distance from a node to its first prime-number descendant in a binary tree defined as: root = 1 and, for any node n, the left child = 2*n and right child = 2*n + 1. The number of primes among the nodes of depth m is equal to A036378(m) for m>=2. %F A338884 a(n) = bitlength(A208241(n)) - bitlength(n), where bitlength = A070939. - _Kevin Ryde_, Nov 13 2020 %o A338884 (Python) %o A338884 from sympy import isprime %o A338884 for n in range(1,101): %o A338884 a = 0 %o A338884 k = i = 1 %o A338884 while isprime(i) == 0: %o A338884 a += 1 %o A338884 k = 2*k %o A338884 for i in range(k*n + 1, k*n + k): %o A338884 if isprime(i) == 1: break %o A338884 print(a) %Y A338884 Cf. A000040, A036378, A208241, A005097 (where a(n)=1). %Y A338884 Cf. A108234 (zero or more bits). %K A338884 nonn %O A338884 1,4 %A A338884 _Ya-Ping Lu_, Nov 13 2020