A282536 Numbers k such that (26*10^k + 49)/3 is prime.

1, 2, 5, 6, 18, 25, 34, 67, 73, 98, 287, 380, 544, 748, 911, 947, 978, 2480, 3017, 7951, 13081, 17665, 17798, 34857, 43960, 100566

Offset

1,2

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 6 followed by the digits 83 is prime (see Example section).

a(27) > 3*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 86w83.

Example

2 is in this sequence because (26*10^2 + 49)/3 = 883 is prime.
Initial terms and associated primes:
a(1) = 1, 103;
a(2) = 2, 883;
a(3) = 5, 866683;
a(4) = 6, 8666683;
a(5) = 18, 8666666666666666683; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(26*10^# + 49)/3] &]

Prog

(PARI) isok(k) = isprime((26*10^k + 49)/3); \\ Michel Marcus, Feb 18 2017

Crossrefs

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

Sequence in context: A319756 A202854 A274911 * A248719 A184594 A341756

Adjacent sequences: A282533 A282534 A282535 * A282537 A282538 A282539

Keyword

nonn,more,hard

Author

Robert Price, Feb 17 2017

Extensions

a(26) from Robert Price, Jul 31 2019

Status

approved