A290476 Numbers k such that (38*10^k + 691)/9 is prime.

2, 4, 8, 10, 14, 16, 29, 106, 179, 197, 365, 371, 557, 857, 862, 1163, 1454, 2206, 5075, 22384, 149999, 196792

Offset

1,1

Comments

For k > 1, numbers such that the digit 4 followed by k - 2 occurrences of the digit 2 followed by the digits 99 is prime (see Example section).

There are no multiples of 3 in the sequence, since (38 * 10^k + 691)/9 is a multiple of 3 if k is.

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 42w99.

Example

4 is in this sequence because (38*10^4 + 691)/9 = 42299 is prime.
Initial terms and primes associated:
a(1) = 2, 499;
a(2) = 4, 42299;
a(3) = 8, 422222299;
a(4) = 10; 42222222299;
a(5) = 14, 422222222222299; etc.

Mathematica

Select[Range[1000], PrimeQ[(38*10^# + 691)/9] &]

Crossrefs

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

Sequence in context: A125499 A240092 A153974 * A189670 A341822 A363797

Adjacent sequences: A290473 A290474 A290475 * A290477 A290478 A290479

Keyword

nonn,more,hard

Author

Robert Price, Aug 03 2017

Extensions

a(21)-a(22) from Robert Price, Oct 31 2018

Status

approved