A295393 Numbers k such that 5*10^k + 23 is prime.

1, 2, 3, 4, 10, 11, 15, 43, 51, 110, 164, 303, 824, 3160, 4994, 8596, 11717, 22370, 22600, 65509, 117205, 149907

Offset

1,2

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 0 followed by the digits 23 is prime (see Example section).

a(23) > 2*10^5.

Links

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

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

Makoto Kamada, Search for 50w23.

Example

2 is in this sequence because 5*10^2 + 23 = 523 is prime.
Initial terms and associated primes:
a(1) = 1, 73;
a(2) = 2, 523;
a(3) = 3, 5023;
a(4) = 4, 50023;
a(5) = 10, 50000000023; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[5*10^# + 23] &]

Prog

(PARI) isok(k) = isprime(5*10^k + 23); \\ Michel Marcus, Nov 22 2017

Crossrefs

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

Sequence in context: A336193 A202426 A039002 * A120023 A353243 A115897

Adjacent sequences: A295390 A295391 A295392 * A295394 A295395 A295396

Keyword

nonn,more,hard,changed

Author

Robert Price, Nov 21 2017

Extensions

a(21)-a(22) from Robert Price, Mar 18 2019

Status

approved