A294938 Numbers k such that (79*10^k - 1)/3 is prime.

1, 2, 5, 11, 23, 38, 59, 77, 79, 413, 919, 1079, 1343, 3194, 5168, 6266, 12710, 18711, 47185, 82347, 170901, 180710

Offset

1,2

Comments

For k > 1, numbers k such that the digits 26 followed by k occurrences of the digit 3 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 263w.

Example

2 is in this sequence because (79*10^2 - 1)/3 = 2633 is prime.
Initial terms and associated primes:
a(1) = 1, 263;
a(2) = 2, 2633;
a(3) = 5, 2633333;
a(4) = 11, 2633333333333;
a(5) = 23, 2633333333333333333333333; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(79*10^# - 1)/3] &]

Prog

(PARI) isok(k) = isprime((79*10^k - 1)/3); \\ Michel Marcus, Nov 12 2017

Crossrefs

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

Sequence in context: A226843 A057931 A039693 * A062475 A186265 A225947

Adjacent sequences: A294935 A294936 A294937 * A294939 A294940 A294941

Keyword

nonn,more,hard

Author

Robert Price, Nov 11 2017

Extensions

a(21)-a(22) from Robert Price, Jan 31 2020

Status

approved