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 A329875 #6 Nov 23 2019 12:05:08
%S A329875 1,3,7,23,151,919,8087,90007,2449303,6643607,115695511,786784151,
%T A329875 2934267799,183322894231,1007956615063,4306491498391,101063514742679,
%U A329875 2634338305138583,106217129734659991,2267944950872498071,69137392218069622679,2504107609947730435991
%N A329875 a(1) = 1, for n > 0, a(n+1) is the least prime number > a(n) whose binary expansion ends with the binary expansion of a(n).
%C A329875 This sequence is a binary variant of A053582.
%C A329875 Dirichlet's theorem on arithmetic progressions guaranties that this sequence is infinite.
%C A329875 We can build a similar sequence for any base b > 1 and any starting value coprime to b.
%e A329875 The first terms, alongside their binary representations, are:
%e A329875 n a(n) bin(a(n))
%e A329875 - ------- ----------------------
%e A329875 1 1 1
%e A329875 2 3 11
%e A329875 3 7 111
%e A329875 4 23 10111
%e A329875 5 151 10010111
%e A329875 6 919 1110010111
%e A329875 7 8087 1111110010111
%e A329875 8 90007 10101111110010111
%e A329875 9 2449303 1001010101111110010111
%o A329875 (PARI) print1 (v=1); for (n=2, 22, forstep (w=v+s=(b=2)^#digits(v,b), oo, s, if (isprime(w), print1 (", "v=w); break)))
%Y A329875 Cf. A053582, A329877.
%K A329875 nonn,base
%O A329875 1,2
%A A329875 _Rémy Sigrist_, Nov 23 2019