%I #42 May 02 2024 04:26:24

%S 1,3,9,12,18,19,36,37,49,67,337,893,1924,8044,11610,13560,18777,35376,

%T 53601,56022,66488,89801,190210

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

%C a(15) > 10000. - _Felix Fröhlich_, Jul 03 2016

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 70w13</a>.

%e 3 is in this sequence because 7*10^3 + 13 = 7013 is prime.

%e 4 is not in the sequence because 7*10^4 + 13 = 70013 = 53 * 1321.

%e Initial terms and associated primes:

%e a(1) = 1: 83;

%e a(2) = 3: 7013;

%e a(3) = 9: 7000000013;

%e a(4) = 12: 7000000000013, etc.

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

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

%o (Magma) [n: n in [1..800] | IsPrime(7*10^n+13)];

%o (PARI) is(n) = ispseudoprime(7*10^n+13) \\ _Felix Fröhlich_, Jul 03 2016

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+13), print1(n, ", "))); \\ _Altug Alkan_, Jul 03 2016

%Y 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).

%K nonn,more

%O 1,2

%A _Vincenzo Librandi_, Jul 03 2016

%E a(15) from _Michael S. Branicky_, Jan 22 2023

%E a(16)-a(17) from _Michael S. Branicky_, Apr 10 2023

%E a(18)-a(23) from Kamada data by _Tyler Busby_, Apr 15 2024