A274238 Numbers k such that (26*10^k - 119)/3 is prime.

1, 2, 3, 4, 6, 22, 25, 29, 59, 89, 221, 453, 535, 1708, 2242, 2413, 3581, 4234, 4848, 5380, 6548, 8654, 11035, 17308, 27634, 28807, 35481, 79678, 80875, 114658, 230394

Offset: 1

Author

Robert Price, Jul 06 2016

Keywords

• nonn
• more

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 6 followed by the digits 27 is prime (see Example section).

a(32) > 3*10^5.

Examples

			3 is in this sequence because (26*10^3 - 119)/3 = 8627 is prime.
Initial terms and associated primes:
a(1) = 1, 47;
a(2) = 2, 827;
a(3) = 3, 8627;
a(4) = 4, 86627;
a(5) = 6, 8666627, etc.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 86w27.

Crossrefs

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

Programs

Magma

[n: n in [1..500] |IsPrime((26*10^n-119) div 3)]; // Vincenzo Librandi, Jul 07 2016

Mathematica

Select[Range[0, 100000], PrimeQ[(26*10^# - 119)/3] &]

PARI

lista(nn) = for(n=1, nn, if(ispseudoprime((26*10^n-119)/3), print1(n, ", "))); \\ Altug Alkan, Jul 08 2016

Extensions

a(30)-a(31) from Robert Price, Jul 12 2023