A282810 Numbers k such that (26*10^k - 77)/3 is prime.

1, 3, 5, 7, 11, 12, 15, 27, 36, 108, 110, 115, 127, 155, 958, 2782, 3090, 6520, 9857, 14543, 21919, 23659, 24727, 49039, 92546, 114317, 131180, 146856, 204730, 219639, 238157

Offset

1,2

Comments

For k > 1, numbers k such that the digit 8 followed by k-2 occurrences of the digit 6 followed by the digits 41 is prime (see Example section).

a(32) > 3*10^5.

Links

Table of n, a(n) for n=1..31.

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

Makoto Kamada, Search for 86w41.

Example

3 is in this sequence because (26*10^3 - 77)/3 = 8641 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 3, 8641;
a(3) = 5, 866641;
a(4) = 7, 86666641;
a(5) = 11, 866666666641; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(26*10^# - 77)/3] &]

Crossrefs

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

Sequence in context: A152212 A347465 A249370 * A102941 A114235 A285848

Adjacent sequences: A282807 A282808 A282809 * A282811 A282812 A282813

Keyword

nonn,more,hard

Author

Robert Price, Feb 22 2017

Extensions

a(26)-a(28) from Robert Price, Nov 15 2019

a(29)-a(31) from Robert Price, Jul 12 2023

Status

approved