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

%I A274676 #42 May 02 2024 04:26:24
%S A274676 1,3,9,12,18,19,36,37,49,67,337,893,1924,8044,11610,13560,18777,35376,
%T A274676 53601,56022,66488,89801,190210
%N A274676 Numbers k such that 7*10^k + 13 is prime.
%C A274676 a(15) > 10000. - _Felix Fröhlich_, Jul 03 2016
%H A274676 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 70w13</a>.
%e A274676 3 is in this sequence because 7*10^3 + 13 = 7013 is prime.
%e A274676 4 is not in the sequence because 7*10^4 + 13 = 70013 = 53 * 1321.
%e A274676 Initial terms and associated primes:
%e A274676 a(1) =  1: 83;
%e A274676 a(2) =  3: 7013;
%e A274676 a(3) =  9: 7000000013;
%e A274676 a(4) = 12: 7000000000013, etc.
%p A274676 select(t -> isprime(7*10^t+13), [$1..2000]); # _Robert Israel_, Jul 03 2016
%t A274676 Select[Range[0, 3000], PrimeQ[7 * 10^# + 13] &]
%o A274676 (Magma) [n: n in [1..800] | IsPrime(7*10^n+13)];
%o A274676 (PARI) is(n) = ispseudoprime(7*10^n+13) \\ _Felix Fröhlich_, Jul 03 2016
%o A274676 (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+13), print1(n, ", "))); \\ _Altug Alkan_, Jul 03 2016
%Y A274676 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 A274676 nonn,more
%O A274676 1,2
%A A274676 _Vincenzo Librandi_, Jul 03 2016
%E A274676 a(15) from _Michael S. Branicky_, Jan 22 2023
%E A274676 a(16)-a(17) from _Michael S. Branicky_, Apr 10 2023
%E A274676 a(18)-a(23) from Kamada data by _Tyler Busby_, Apr 15 2024