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Numbers k such that 7*10^k + 33 is prime.
1

%I #22 Jun 02 2024 14:03:16

%S 1,2,6,10,17,29,53,107,133,596,852,1068,1186,1356,1673,1987,3170,3312,

%T 5819,6655,19267,20009,29302,72614,170348,178566

%N Numbers k such that 7*10^k + 33 is prime.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 70w33</a>.

%e 2 is in this sequence because 7*10^2 + 33 = 733 is prime.

%e 4 is not in the sequence because 7*10^4 + 33 = 70033 = 59 * 1187.

%e Initial terms and associated primes:

%e a(1) = 1: 103;

%e a(2) = 2: 733;

%e a(3) = 6: 7000033;

%e a(4) = 10: 70000000033, etc.

%t Select[Range[0, 3000], PrimeQ[7 10^# + 33] &]

%o (Magma) [n: n in [1..500] | IsPrime(7*10^n+33)];

%o (PARI) lista(nn) = for(n=1, nn, if(ispseudoprime(7*10^n+33), print1(n, ", "))); \\ _Altug Alkan_, Jul 05 2016

%Y Cf. similar sequences listed in A274676.

%K nonn,more

%O 1,2

%A _Vincenzo Librandi_, Jul 04 2016

%E a(19)-a(20) from _Michael S. Branicky_, Aug 16 2021

%E a(21)-a(26) from Kamada data by _Tyler Busby_, Apr 14 2024