A294374 Numbers k such that (44*10^k - 413)/9 is prime.

1, 2, 8, 9, 12, 17, 23, 26, 51, 113, 236, 509, 1659, 2769, 5258, 8456, 8787, 11487, 19367, 28094, 36114, 69663, 115697

Offset

1,2

Comments

For k>1, numbers such that the digit 4 followed by k-2 occurrences of the digit 8 followed by the digits 43 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 48w43

Example

2 is in this sequence because (44*10^2 - 413)/9 = 443 is prime.
Initial terms and primes associated:
a(1) = 1, 3;
a(2) = 2, 443;
a(3) = 8, 488888843;
a(4) = 9, 4888888843;
a(5) = 12, 4888888888843; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(44*10^# - 413)/9] &]

Crossrefs

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

Sequence in context: A086678 A359771 A289146 * A066550 A162952 A033950

Adjacent sequences: A294371 A294372 A294373 * A294375 A294376 A294377

Keyword

nonn,more,hard

Author

Robert Price, Oct 29 2017

Extensions

a(23) from Robert Price, Mar 03 2019

Status

approved