A295030 Numbers k such that 4*10^k + 91 is prime.

1, 2, 3, 8, 10, 15, 31, 32, 77, 106, 191, 197, 525, 557, 1958, 3848, 12771, 13348, 13507, 23164, 55932, 67375, 68020, 95407, 95672, 109142, 113905, 150577, 185905, 261248

Offset

1,2

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 91 is prime (see Example section).

a(31) > 3*10^5.

Links

Table of n, a(n) for n=1..30.

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

Makoto Kamada, Search for 40w91.

Example

2 is in this sequence because 4*10^2 + 91 = 491 is prime.
Initial terms and associated primes:
a(1) = 1, 131;
a(2) = 2, 491;
a(3) = 3, 4091;
a(4) = 8, 400000091;
a(5) = 10, 40000000091; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[4*10^# + 91] &]

Prog

(PARI) isok(k) = isprime(4*10^k + 91); \\ Michel Marcus, Nov 13 2017

Crossrefs

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

Sequence in context: A286092 A100317 A376266 * A317655 A060697 A326714

Adjacent sequences: A295027 A295028 A295029 * A295031 A295032 A295033

Keyword

nonn,more,hard

Author

Robert Price, Nov 12 2017

Extensions

a(26)-a(29) from Robert Price, Aug 18 2018

a(30) from Robert Price, Jun 01 2023

Status

approved