A290577 Numbers k such that 3*10^k - 97 is prime.

3, 5, 6, 7, 28, 42, 45, 59, 69, 179, 271, 293, 621, 851, 2632, 2764, 5811, 6813, 7974, 17015, 30449, 32760, 43939, 85227, 87573, 93179, 122345, 156435, 174665, 177373, 292344

Offset

1,1

Comments

For k > 1, numbers k such that the digit 2 followed by k-2 occurrences of the digit 9 followed by the digits 03 is prime (see Example section).

a(32) > 3*10^5.

Links

Table of n, a(n) for n=1..31.

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

Makoto Kamada, Search for 29w03.

Example

5 is in this sequence because 3*10^5 - 97 = 299903 is prime.
Initial terms and associated primes:
a(1) = 3, 2903;
a(2) = 5, 299903;
a(3) = 6, 2999903;
a(4) = 7; 29999903;
a(5) = 28, 29999999999999999999999999903; etc.

Mathematica

Select[Range[2, 100000], PrimeQ[3*10^# - 97] &]

Prog

(PARI) isok(n) = isprime(3*10^n - 97); \\ Michel Marcus, Aug 07 2017

Crossrefs

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

Sequence in context: A250419 A072134 A179220 * A145736 A188195 A337092

Adjacent sequences: A290574 A290575 A290576 * A290578 A290579 A290580

Keyword

nonn,more,hard

Author

Robert Price, Aug 06 2017

Extensions

a(27)-a(30) from Robert Price, Jul 18 2018

a(31) from Robert Price, Jun 17 2023

Status

approved