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 A335302 #9 Jun 02 2020 14:09:43
%S A335302 1,5,3,11,5,17,3,7,13,3,37,9,3,7,21,11,5,67,7,9,7,19,9,33,5,3,11,5,17,
%T A335302 15,131,9,3,21,3,13,35,7,13,19,5,15,65,5,3,19,15,35,5,9,7,17,11,257,7,
%U A335302 13,3,21,9,3,37,19,7,9,5,75,17,11,5,33,7,15,21,11
%N A335302 a(n) = prime(n+1) mod (2^k) where k is the least positive integer such that floor(prime(n)/(2^k)) = floor(prime(n+1)/(2^k)) and prime(n) denotes the n-th prime number.
%C A335302 In other words, the binary representation of a(n) is the smallest suffix to be overlaid on the binary representation of the n-th prime number to obtain that of the next prime number.
%C A335302 This sequence has similarities with A006519; here we consider consecutive prime numbers, there consecutive nonnegative integers.
%C A335302 There are no two consecutive equal terms.
%H A335302 Rémy Sigrist, <a href="/A335302/b335302.txt">Table of n, a(n) for n = 1..10000</a>
%F A335302 a(n) <= prime(n+1) with equality iff prime(n+1) belongs to A014210.
%e A335302 The first terms, alongside the binary representations of a(n) and of prime(n+1), are:
%e A335302 n a(n) bin(a(n)) bin(prime(n+1))
%e A335302 -- ---- --------- ---------------
%e A335302 0 N/A N/A 10
%e A335302 1 1 1 11
%e A335302 2 5 101 101
%e A335302 3 3 11 111
%e A335302 4 11 1011 1011
%e A335302 5 5 101 1101
%e A335302 6 17 10001 10001
%e A335302 7 3 11 10011
%e A335302 8 7 111 10111
%e A335302 9 13 1101 11101
%e A335302 10 3 11 11111
%o A335302 (PARI) { base=2; p=2; forprime (q=p+1, 379, for (k=0, oo, m=base^k; if (q\m == p\m, print1 (q%m", "); p=q; break))) }
%Y A335302 Cf. A006519, A014210, A335301 (decimal variant).
%K A335302 nonn,base
%O A335302 1,2
%A A335302 _Rémy Sigrist_, May 31 2020