A294942 Numbers k such that (74*10^k + 313)/9 is prime.

0, 2, 6, 15, 18, 26, 51, 75, 86, 114, 257, 275, 537, 753, 914, 1944, 18431, 18741, 21281, 28272, 31002, 71621, 84170, 110961

Offset

1,2

Comments

For k > 1, numbers such that the digit 8 followed by k-2 occurrences of the digit 2 followed by the digits 57 is prime (see Example section).

a(25) > 2*10^5.

Links

Table of n, a(n) for n=1..24.

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

Makoto Kamada, Search for 82w57.

Example

2 is in this sequence because (74*10^2 + 313)/9 = 857 is prime.
Initial terms and primes associated:
a(1) = 0, 43;
a(2) = 2, 857;
a(3) = 6, 8222257;
a(4) = 15, 8222222222222257;
a(5) = 18, 8222222222222222257; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(74*10^# + 313)/9] &]

Prog

(PARI) isok(k) = isprime((74*10^k + 313)/9); \\ Michel Marcus, Nov 12 2017

Crossrefs

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

Sequence in context: A020947 A011777 A324176 * A227307 A129631 A014847

Adjacent sequences: A294939 A294940 A294941 * A294943 A294944 A294945

Keyword

nonn,more,hard

Author

Robert Price, Nov 11 2017

Extensions

a(24) from Robert Price, Jun 14 2019

Status

approved