A256228 Numbers k such that 4*10^k - 21 is prime.

1, 2, 4, 5, 7, 9, 10, 17, 21, 41, 51, 59, 61, 77, 79, 83, 97, 108, 427, 615, 869, 900, 966, 3150, 3239, 3932, 5218, 11941, 30558, 44697, 90334, 113874, 128343, 142810, 222253

Offset: 1

Author

Robert Price, Apr 17 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers that begin with the digit 3 followed by k-2 occurrences of the digit 9 followed by the digits 79 are prime (see Example section).

a(36) > 3*10^5.

Examples

			4 is in this sequence because 4*10^4 - 21 = 39979, which is prime.
Initial terms and associated primes:
a(1) = 1, 19;
a(2) = 2, 379;
a(3) = 4, 39979;
a(4) = 5, 399979;
a(5) = 7, 39999979, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 39w79.

Crossrefs

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

Programs

Mathematica

Select[Range[1, 100000], PrimeQ[4*10^# - 21] &]

PARI

is(n)=ispseudoprime(4*10^n - 21) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

a(32)-a(34) from Robert Price, Sep 10 2018

a(35) from Robert Price, Jun 01 2023