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 A234310 Primes of the form 4^k + 4^m - 1, where k and m are positive integers. 14
 7, 19, 31, 67, 79, 127, 271, 1039, 1087, 1279, 4099, 4111, 4159, 5119, 8191, 16447, 20479, 65539, 65551, 65599, 81919, 131071, 262147, 262399, 263167, 266239, 524287, 1049599, 1114111, 1310719, 4194319, 4194559, 4195327, 16842751, 17825791, 67108879 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Clearly each term is congruent to 1 modulo 6. By the conjecture in A234309, this sequence should have infinitely many terms. Note that any Mersenne prime greater than 3 has the form 2^{2*k+1} - 1 = 4^k + 4^k - 1, where k is a positive integer. LINKS Zhi-Wei Sun, Table of n, a(n) for n = 1..800 EXAMPLE a(1) = 7 since 7 = 4^1 + 4^1 - 1 is prime. a(2) = 19 since 19 = 4^1 + 4^2 - 1 is prime. a(3) = 31 since 31 = 4^2 + 4^2 - 1 is prime. MATHEMATICA n=0; Do[If[PrimeQ[4^k+4^m-1], n=n+1; Print[n, " ", 4^m+4^k-1]], {m, 1, 250}, {k, 1, m}] PROG (PARI) for(k=1, 30, for(m=1, k, if(ispseudoprime(t=4^k+4^m-1), print1(t", ")))) \\ Charles R Greathouse IV, Dec 23 2013 CROSSREFS Cf. A000040, A000302, A000668, A233346, A233393, A234309. Sequence in context: A216532 A249375 A212492 * A141338 A237366 A216531 Adjacent sequences:  A234307 A234308 A234309 * A234311 A234312 A234313 KEYWORD nonn AUTHOR Zhi-Wei Sun, Dec 23 2013 STATUS approved

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Last modified August 18 01:19 EDT 2019. Contains 326059 sequences. (Running on oeis4.)