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).

1, 3, 7, 23, 151, 919, 8087, 90007, 2449303, 6643607, 115695511, 786784151, 2934267799, 183322894231, 1007956615063, 4306491498391, 101063514742679, 2634338305138583, 106217129734659991, 2267944950872498071, 69137392218069622679, 2504107609947730435991

Offset: 1

Author

Rémy Sigrist, Nov 23 2019

Keywords

• nonn
• base

Comments

This sequence is a binary variant of A053582.

Dirichlet's theorem on arithmetic progressions guaranties that this sequence is infinite.

We can build a similar sequence for any base b > 1 and any starting value coprime to b.

Examples

			The first terms, alongside their binary representations, are:
  n  a(n)     bin(a(n))
  -  -------  ----------------------
  1        1                       1
  2        3                      11
  3        7                     111
  4       23                   10111
  5      151                10010111
  6      919              1110010111
  7     8087           1111110010111
  8    90007       10101111110010111
  9  2449303  1001010101111110010111
		

Crossrefs

Cf. A053582, A329877.

Programs

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)))