A278707 Numbers k such that (7*10^k - 313) / 9 is prime.

2, 3, 5, 6, 9, 14, 18, 21, 24, 27, 29, 83, 513, 555, 750, 843, 1118, 4494, 5886, 6968, 9519, 12290, 15779, 76536, 76818, 90371

Offset

1,1

Comments

For n>1, numbers such that n-2 occurrences of the digit 7 followed by the digits 43 is prime (see Example section).

a(27) > 2*10^5.

Links

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 7w43.

Example

3 is in this sequence because (7*10^3 - 313) / 9 = 743 is prime.
Initial terms and primes associated:
a(1) = 2, 43;
a(2) = 3, 743;
a(3) = 5, 77743;
a(4) = 6, 777743;
a(5) = 9, 777777743; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(7*10^# - 313) / 9] &]

Prog

(PARI) isok(n) = isprime((7*10^n - 313) / 9); \\ Michel Marcus, Nov 27 2016
(Magma) [n: n in [0..500] | IsPrime((7*10^n-313) div 9)]; // Vincenzo Librandi, Nov 27 2016

Crossrefs

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

Sequence in context: A073216 A181902 A295631 * A294631 A059454 A138538

Adjacent sequences: A278704 A278705 A278706 * A278708 A278709 A278710

Keyword

nonn,more,hard

Author

Robert Price, Nov 26 2016

Status

approved