A294227 Numbers k such that (16*10^k + 167)/3 is prime.

0, 1, 5, 8, 12, 13, 14, 15, 33, 98, 123, 260, 485, 1340, 1674, 1775, 5988, 7039, 9421, 15149, 21751, 30882, 36517, 85839, 121633, 131180, 140091, 188823

Offset

1,3

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 89 is prime (see Example section).

a(29) > 2*10^5.

Links

Table of n, a(n) for n=1..28.

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

Makoto Kamada, Search for 53w89.

Example

5 is in this sequence because (16*10^5 + 167)/3 = 533389 is prime.
Initial terms and associated primes:
a(1) = 0, 61;
a(2) = 1, 109;
a(3) = 5, 533389;
a(4) = 8, 533333389;
a(5) = 12, 5333333333389; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(16*10^# + 167)/3] &]

Crossrefs

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

Sequence in context: A247245 A319675 A076635 * A116602 A079896 A133315

Adjacent sequences: A294224 A294225 A294226 * A294228 A294229 A294230

Keyword

nonn,more,hard

Author

Robert Price, Oct 25 2017

Extensions

a(25)-a(28) from Robert Price, Jun 18 2019

Status

approved