A294943 Numbers k such that (865*10^k - 1)/9 is prime.

7, 13, 25, 40, 58, 133, 229, 232, 310, 358, 778, 977, 1057, 1271, 4417, 4757, 5242, 6413, 11539, 60583, 149737

Offset

1,1

Comments

For k > 1, numbers k such that the digits 96 followed by k occurrences of the digit 1 is prime (see Example section).

a(22) > 2*10^5.

Links

Table of n, a(n) for n=1..21.

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

Makoto Kamada, Search for 961w.

Example

7 is in this sequence because (865*10^7 - 1)/9 = 961111111 is prime.
Initial terms and associated primes:
a(1) = 7, 961111111;
a(2) = 12, 961111111111111;
a(3) = 23, 961111111111111111111111111;
a(4) = 40, 961111111111111111111111111111111111111111;  etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(865*10^# - 1)/9] &]

Prog

(PARI) isok(k) = isprime((865*10^k - 1)/9); \\ Michel Marcus, Nov 12 2017

Crossrefs

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

Sequence in context: A362632 A200270 A031887 * A363080 A111721 A213663

Adjacent sequences: A294940 A294941 A294942 * A294944 A294945 A294946

Keyword

nonn,more,hard

Author

Robert Price, Nov 11 2017

Extensions

a(21) from Robert Price, Apr 18 2020

Status

approved