A280632 Numbers k such that (19*10^k + 191)/3 is prime.

1, 3, 4, 9, 10, 11, 14, 25, 38, 74, 110, 133, 145, 469, 1035, 1808, 3323, 4534, 4875, 5306, 16645, 20591, 25904, 29365, 81488, 108184, 132550

Offset

1,2

Comments

For k>1, numbers such that the digit 6 followed by k-2 occurrences of the digit 3 followed by the digits 97 is prime (see Example section).

a(28) > 2*10^5.

Links

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 63w97.

Example

4 is in this sequence because (19*10^4 + 191) / 3 = 63397 is prime.
Initial terms and primes associated:
a(1) = 1, 127;
a(2) = 3, 6397;
a(3) = 4, 63397;
a(4) = 9, 6333333397;
a(5) = 10, 63333333397; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(19*10^# + 191) / 3] &]

Prog

(PARI) isok(n) = isprime((19*10^n + 191)/3); \\ Michel Marcus, Jan 07 2017

Crossrefs

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

Sequence in context: A079258 A134025 A109406 * A178462 A010376 A010388

Adjacent sequences: A280629 A280630 A280631 * A280633 A280634 A280635

Keyword

nonn,more,hard

Author

Robert Price, Jan 06 2017

Extensions

a(26)-a(27) from Robert Price, May 09 2019

Status

approved