A278695 Numbers k such that (38*10^k - 119) / 9 is prime.

1, 2, 4, 5, 8, 14, 16, 17, 20, 22, 38, 134, 136, 152, 829, 1087, 2110, 3524, 4412, 7079, 10538, 17672, 21583, 24163, 35126, 72050

Offset

1,2

Comments

For k>1, numbers such that the digit 4 followed by k-2 occurrences of the digit 2 followed by the digits 09 is prime (see Example section).

a(27) > 2*10^5.

Links

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

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

Makoto Kamada, Search for 42w09.

Example

4 is in this sequence because (38*10^4 - 119) / 9 = 42209 is prime.
Initial terms and primes associated:
a(1) = 1, 29;
a(2) = 2, 409;
a(3) = 4, 42209;
a(4) = 5, 422209;
a(5) = 8, 422222209; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(38*10^# - 119) / 9] &]

Prog

(PARI) isok(n) = isprime((38*10^n - 119) / 9); \\ Michel Marcus, Nov 27 2016

Crossrefs

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

Sequence in context: A288668 A264800 A293189 * A105134 A226791 A357177

Adjacent sequences: A278692 A278693 A278694 * A278696 A278697 A278698

Keyword

nonn,more,hard

Author

Robert Price, Nov 26 2016

Status

approved