A271645 Numbers k such that (23*10^k + 91)/3 is prime.

1, 2, 4, 15, 16, 19, 20, 26, 38, 47, 52, 75, 122, 191, 246, 257, 294, 305, 374, 592, 682, 729, 1092, 2053, 2997, 4065, 13936, 17214, 19059, 37433, 142105, 214633, 242909

Offset

1,2

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 6 followed by the digits 97 is prime (see Example section).

a(34) > 3*10^5.

Links

Table of n, a(n) for n=1..33.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 76w97.

Example

4 is in this sequence because (23*10^4 + 91)/3 = 76697 is prime.
Initial terms and associated primes:
a(1) = 1, 107;
a(2) = 2, 797;
a(3) = 4, 76697;
a(4) = 15, 7666666666666697;
a(5) = 16, 76666666666666697, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(23*10^# + 91)/3] &]

Prog

(PARI) is(n)=ispseudoprime((23*10^n + 91)/3) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Sequence in context: A196239 A019543 A304568 * A265483 A357692 A154906

Adjacent sequences: A271642 A271643 A271644 * A271646 A271647 A271648

Keyword

nonn,more,changed

Author

Robert Price, Apr 11 2016

Extensions

a(31) from Robert Price, Aug 11 2019

a(32)-a(33) from Robert Price, May 31 2023

Status

approved