A294945 Numbers k such that 6*10^k - 91 is prime.

2, 6, 25, 30, 45, 98, 296, 498, 627, 1001, 1995, 1998, 2518, 3208, 3753, 4130, 7159, 7660, 10840, 16187, 24744, 28345, 31499, 32999, 44838, 60959, 88938, 209846

Offset

1,1

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 9 followed by the digits 09 is prime (see Example section).

a(29) > 3*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 59w09.

Example

2 is in this sequence because 6*10^2 - 91 = 509 is prime.
Initial terms and associated primes:
a(1) = 2, 509;
a(2) = 6, 5999909;
a(3) = 25, 59999999999999999999999909;
a(4) = 30, 5999999999999999999999999999909;
a(5) = 45, 5999999999999999999999999999999999999999999909; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[6*10^# - 91] &]

Prog

(PARI) isok(k) = isprime(6*10^k - 91); \\ Michel Marcus, Nov 12 2017

Crossrefs

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

Sequence in context: A123150 A086591 A173609 * A353363 A073545 A103063

Adjacent sequences: A294942 A294943 A294944 * A294946 A294947 A294948

Keyword

nonn,more,hard,changed

Author

Robert Price, Nov 11 2017

Extensions

Terms reordered into ascending order by Robert Price, Apr 03 2022

a(28) from Robert Price, Jul 12 2023

Status

approved