A295631 Numbers k such that (38*10^k + 187)/9 is prime.

2, 3, 5, 6, 9, 14, 17, 20, 54, 56, 165, 902, 1023, 6483, 14174, 18411, 20025, 27411, 49583, 59589, 66896, 97329

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 43 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 42w43

Example

2 is in this sequence because (38*10^2 + 187)/9 = 443 is prime.
Initial terms and primes associated:
a(1) = 2, 443;
a(2) = 3, 4243;
a(3) = 5, 422243;
a(4) = 6, 4222243;
a(5) = 9, 4222222243; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[38*10^# + 187)/9] &]
Select[Range[2, 100000], PrimeQ[100*FromDigits[PadRight[{4}, #-1, 2]]+43]&] (* Harvey P. Dale, Jan 16 2018 *)

Prog

(PARI) is(k) = ispseudoprime((38*10^k + 187)/9) \\ Iain Fox, Nov 24 2017

Crossrefs

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

Sequence in context: A175095 A073216 A181902 * A278707 A294631 A059454

Adjacent sequences: A295628 A295629 A295630 * A295632 A295633 A295634

Keyword

nonn,more,hard

Author

Robert Price, Nov 24 2017

Status

approved