A293274 Numbers k such that (23*10^k - 47)/3 is prime.

1, 2, 4, 5, 11, 28, 34, 35, 36, 49, 65, 90, 126, 1878, 2089, 3266, 3818, 6485, 7710, 8539, 20603, 34764, 51283, 176964, 258494

Offset

1,2

Comments

For k > 1, numbers k such that the digit 7 followed by k-2 occurrences of the digit 6 followed by the digits 51 is prime (see Example section).

a(26) > 3*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 76w51.

Example

4 is in this sequence because (23*10^4 - 47)/3 = 76651 is prime.
Initial terms and associated primes:
a(1) = 1, 61;
a(2) = 2, 751;
a(3) = 4, 76651;
a(4) = 5, 766651;
a(5) = 11, 766666666651; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(23*10^# - 47)/3] &]

Crossrefs

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

Sequence in context: A095022 A279050 A317828 * A101961 A285055 A344712

Adjacent sequences: A293271 A293272 A293273 * A293275 A293276 A293277

Keyword

nonn,more,hard

Author

Robert Price, Oct 04 2017

Extensions

a(24) from Robert Price, Sep 22 2019

a(25) from Robert Price, Oct 25 2023

Status

approved