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

1,2

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.

Links

Table of n, a(n) for n=1..22.

Example

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

Prog

(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)))

Crossrefs

Cf. A053582, A329877.

Sequence in context: A133788 A120271 A145938 * A048721 A113824 A121883

Adjacent sequences: A329872 A329873 A329874 * A329876 A329877 A329878

Keyword

nonn,base

Author

Rémy Sigrist, Nov 23 2019

Status

approved