A294635 Numbers k such that (536*10^k - 23)/9 is prime.

1, 2, 5, 7, 8, 11, 17, 61, 73, 89, 197, 233, 308, 2096, 3170, 8003, 15014, 16166, 26021, 55748, 102533, 171601

Offset

1,2

Comments

For k>1, numbers k such that the digits 59 followed by k-1 occurrences of the digit 5 followed by the digit 3 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 595w3.

Example

2 is in this sequence because (536*10^2 - 23)/9 = 5953 is prime.
Initial terms and associated primes:
a(1) = 1, 593;
a(2) = 2, 5953;
a(3) = 5, 5955553;
a(4) = 7, 595555553;
a(5) = 8, 5955555553; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(536*10^# - 23)/9] &]

Crossrefs

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

Sequence in context: A285938 A325441 A192111 * A362591 A032402 A299326

Adjacent sequences: A294632 A294633 A294634 * A294636 A294637 A294638

Keyword

nonn,more,hard

Author

Robert Price, Nov 05 2017

Extensions

a(21)-a(22) from Robert Price, Feb 23 2020

Status

approved