A291608 Numbers k such that 56*10^k - 3 is prime.

0, 1, 3, 6, 10, 18, 21, 34, 44, 105, 154, 163, 189, 382, 421, 2473, 2664, 4590, 9804, 19950, 29992, 38457, 40249, 124656, 185139, 195032

Offset

1,3

Comments

For k > 0, numbers k such that the digits 55 followed by k-1 occurrences of the digit 9 followed by the digit 7 is prime (see Example section).

a(27) > 2*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 559w7.

Example

3 is in this sequence because 56*10^3 - 3 = 55997 is prime.
Initial terms and associated primes:
a(1) = 0, 53;
a(2) = 1, 557;
a(3) = 3, 55997;
a(4) = 6, 55999997;
a(5) = 10, 559999999997; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[56*10^# - 3] &]

Crossrefs

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

Sequence in context: A259968 A242525 A266617 * A182152 A170803 A182908

Adjacent sequences: A291605 A291606 A291607 * A291609 A291610 A291611

Keyword

nonn,more,hard

Author

Robert Price, Aug 27 2017

Extensions

a(24)-a(26) from Robert Price, Mar 17 2020

Status

approved