A295083 Numbers k such that (115*10^k - 7)/9 is prime.

1, 2, 14, 26, 53, 86, 133, 206, 245, 323, 362, 872, 4562, 12577, 14294, 18425, 21713, 27728, 87368, 106772

Offset

1,2

Comments

For k > 0, numbers such that the digits 12 followed by k occurrences of the digit 7 is prime (see Example section).

a(21) > 2*10^5.

Links

Table of n, a(n) for n=1..20.

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

Makoto Kamada, Search for 127w.

Example

2 is in this sequence because (115*10^2 - 7)/9 = 1277 is prime.
Initial terms and primes associated:
a(1) = 1, 127;
a(2) = 2, 1277;
a(3) = 14, 1277777777777777;
a(4) = 26, 1277777777777777777777777777;  etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(115*10^# - 7)/9] &]
Select[Range[87500], PrimeQ[FromDigits[PadRight[{1, 2}, #, 7]]]&]-2 (* Harvey P. Dale, May 27 2018 *)

Prog

(PARI) isok(k) = isprime((115*10^k - 7)/9); \\ Michel Marcus, Nov 14 2017

Crossrefs

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

Sequence in context: A017545 A280268 A109080 * A180877 A032461 A072390

Adjacent sequences: A295080 A295081 A295082 * A295084 A295085 A295086

Keyword

nonn,more,hard

Author

Robert Price, Nov 13 2017

Extensions

a(20) from Robert Price, Feb 08 2020

Status

approved