A178653 Numbers k that 4^k + 13^2 is prime.
1, 3, 5, 7, 9, 13, 15, 31, 33, 47, 65, 99, 103, 147, 197, 203, 257, 399, 411, 471, 497, 979, 1189, 2851, 3221, 4689, 5027, 7131, 7545, 9049, 9849
Offset: 1
Keywords
Examples
4^1 + 13^2 = 173 = prime(40), 1 is first term. 4^3 + 13^2 = 233 = prime(51), 3 is 2nd term. 4^5 + 13^2 = 1193 = prime(196), 5 is 3rd term. 4^147 + 13^2 = 318286...15753 (89 digits), 147 is 14th term. 4^197 + 13^2 = 403...9753 (119 digits), 197 is 15th term.
Programs
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Mathematica
fQ[n_] := PrimeQ[(2^k)^2 + 169]; k = 1; lst = {}; While[k < 10^4, If[ fQ@k, AppendTo[lst, k]; Print@k]; k += 2]; lst (* Robert G. Wilson v, Jul 31 2010 *) -
PARI
forstep(k=1,999,2,if(ispseudoprime(4^n+169),print1(n", "))) \\ Charles R Greathouse IV, Aug 27 2013
Extensions
a(16)-a(31) from Robert G. Wilson v, Jul 31 2010
New name from Charles R Greathouse IV, Aug 27 2013
Comments