A295392 Numbers k such that 5*10^k + 57 is prime.

1, 2, 5, 8, 14, 23, 24, 26, 41, 62, 85, 137, 209, 446, 1424, 1783, 3301, 5503, 5928, 9593, 18671, 40189, 60655, 113586, 172692

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 57 is prime (see Example section).

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 50w57.

Example

2 is in this sequence because 5*10^2 + 57 = 557 is prime.
Initial terms and associated primes:
a(1) = 1, 107;
a(2) = 2, 557;
a(3) = 5, 500057;
a(4) = 8, 500000057;
a(5) = 14, 500000000000057; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[5*10^# + 57] &]

Prog

(PARI) isok(k) = isprime(5*10^k + 57); \\ Michel Marcus, Nov 22 2017

Crossrefs

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

Sequence in context: A330378 A058578 A261526 * A023674 A281864 A304025

Adjacent sequences: A295389 A295390 A295391 * A295393 A295394 A295395

Keyword

nonn,more,hard

Author

Robert Price, Nov 21 2017

Extensions

a(24)-a(25) from Robert Price, Dec 28 2018

Status

approved