A274676 Numbers k such that 7*10^k + 13 is prime.

1, 3, 9, 12, 18, 19, 36, 37, 49, 67, 337, 893, 1924, 8044, 11610, 13560, 18777, 35376, 53601, 56022, 66488, 89801, 190210

Offset

1,2

Comments

a(15) > 10000. - Felix Fröhlich, Jul 03 2016

Links

Table of n, a(n) for n=1..23.

Makoto Kamada, Search for 70w13.

Example

3 is in this sequence because 7*10^3 + 13 = 7013 is prime.
4 is not in the sequence because 7*10^4 + 13 = 70013 = 53 * 1321.
Initial terms and associated primes:
a(1) =  1: 83;
a(2) =  3: 7013;
a(3) =  9: 7000000013;
a(4) = 12: 7000000000013, etc.

Maple

select(t -> isprime(7*10^t+13), [$1..2000]); # Robert Israel, Jul 03 2016

Mathematica

Select[Range[0, 3000], PrimeQ[7 * 10^# + 13] &]

Prog

(Magma) [n: n in [1..800] | IsPrime(7*10^n+13)];
(PARI) is(n) = ispseudoprime(7*10^n+13) \\ Felix Fröhlich, Jul 03 2016
(PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+13), print1(n, ", "))); \\ Altug Alkan, Jul 03 2016

Crossrefs

Cf. numbers k such that 7*10^k + m is prime: A056804 (m=1), A097970 (m=3), A097954 (m=9), this sequence (m=13), A274677 (m=19), A274678 (m=27), A111021 (m=31), A274679 (m=33), A274700 (m=37), A274692 (m=43), A270974 (m=57).

Sequence in context: A108860 A006499 A310320 * A310321 A310322 A261953

Adjacent sequences: A274673 A274674 A274675 * A274677 A274678 A274679

Keyword

nonn,more

Author

Vincenzo Librandi, Jul 03 2016

Extensions

a(15) from Michael S. Branicky, Jan 22 2023

a(16)-a(17) from Michael S. Branicky, Apr 10 2023

a(18)-a(23) from Kamada data by Tyler Busby, Apr 15 2024

Status

approved