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A274214 Numbers k such that 4*10^k + 63 is prime.

%I A274214 #16 May 02 2024 04:26:59
%S A274214 0,1,2,4,6,9,11,14,16,26,54,74,111,130,152,253,345,607,686,1590,2711,
%T A274214 5462,7021,8681,11044,18132,24072,25211,44332,52792,85881
%N A274214 Numbers k such that 4*10^k + 63 is prime.
%C A274214 For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 0 followed by the digits 63 is prime (see Example section).
%C A274214 a(32) > 2*10^5.
%H A274214 Makoto Kamada, <a href="https://stdkmd.net/nrr">Factorization of near-repdigit-related numbers</a>.
%H A274214 Makoto Kamada, <a href="https://stdkmd.net/nrr/prime/prime_difficulty.txt">Search for 40w63</a>.
%e A274214 4 is in this sequence because 4*10^4 + 63 = 40063 is prime.
%e A274214 Initial terms and associated primes:
%e A274214 a(1) = 0, 67;
%e A274214 a(2) = 1, 103;
%e A274214 a(3) = 2, 463;
%e A274214 a(4) = 4, 40063;
%e A274214 a(5) = 6, 4000063, etc.
%t A274214 Select[Range[0, 100000], PrimeQ[4*10^# + 63] &]
%o A274214 (PARI) is(n)=ispseudoprime(4*10^n + 63) \\ _Charles R Greathouse IV_, Jun 13 2017
%Y A274214 Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.
%K A274214 nonn,more
%O A274214 1,3
%A A274214 _Robert Price_, Jun 13 2016