A290431 Numbers k such that (73*10^k + 413)/9 is prime.

1, 2, 4, 5, 7, 16, 31, 34, 44, 68, 145, 158, 227, 499, 643, 970, 1004, 1951, 2923, 3092, 28069, 48334, 76262

Offset

1,2

Comments

For k > 1, numbers such that the digit 8 followed by k-2 occurrences of the digit 1 followed by the digits 57 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 81w57.

Example

4 is in this sequence because (73*10^4 + 413)/9 = 81157 is prime.
Initial terms and primes associated:
a(1) = 1, 127;
a(2) = 2, 857;
a(3) = 4, 81157;
a(4) = 5, 811157;
a(5) = 7, 81111157; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(73*10^# + 413)/9] &]

Crossrefs

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

Sequence in context: A123210 A019277 A127791 * A220701 A005620 A049915

Adjacent sequences: A290428 A290429 A290430 * A290432 A290433 A290434

Keyword

nonn,more,hard

Author

Robert Price, Oct 06 2017

Status

approved