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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
1, 3, 7, 23, 151, 919, 8087, 90007, 2449303, 6643607, 115695511, 786784151, 2934267799, 183322894231, 1007956615063, 4306491498391, 101063514742679, 2634338305138583, 106217129734659991, 2267944950872498071, 69137392218069622679, 2504107609947730435991 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 29 05:25 EST 2020. Contains 332353 sequences. (Running on oeis4.)