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 A178653 Numbers k that 4^k + 13^2 is prime. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A178652. LINKS Table of n, a(n) for n=1..31. EXAMPLE 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. 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 *) PROG (PARI) forstep(k=1, 999, 2, if(ispseudoprime(4^n+169), print1(n", "))) \\ Charles R Greathouse IV, Aug 27 2013 CROSSREFS Cf. A176969, A176978, A177833, A178652. Sequence in context: A003524 A243910 A211136 * A222314 A228232 A182058 Adjacent sequences: A178650 A178651 A178652 * A178654 A178655 A178656 KEYWORD nonn AUTHOR Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Jun 01 2010 EXTENSIONS a(16)-a(31) from Robert G. Wilson v, Jul 31 2010 New name from Charles R Greathouse IV, Aug 27 2013 STATUS approved

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Last modified August 3 05:44 EDT 2024. Contains 374875 sequences. (Running on oeis4.)