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 A268175 Smallest number k such that k*(2^(2*A000043(n))-1)+1 is prime. 0

%I #19 Apr 09 2016 16:55:42

%S 2,2,4,6,12,82,14,22,244,44,120,94,1010,764,834,1076,516,3252,1384,

%T 1664,7040,6104,20942,14344,37142,12522,12554,64160,32172,44460,49400,

%U 291726

%N Smallest number k such that k*(2^(2*A000043(n))-1)+1 is prime.

%C The numbers k*(2^(2*A000043(n))-1)+1 may be written as k*(2^A000043(n)-1)*(2^A000043(n)+1)+1 or k*Mersenne(n)*(Mersenne(n)+2)+1 and so may be proved primes.

%C All the numbers a(n)*(2^(2*A000043(n)-1)+1 for n=1 to 32 have been proved to be primes.

%e 2*(2^(2*2)-1)+1 = 31 (prime) and A000043(1) = 2, so a(1) = 2.

%e 2*(2^(2*3)-1)+1 = 127 (prime) and A000043(2) = 3, so a(2) = 2.

%t A000043 = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521, 607, 1279, 2203, 2281, 3217, 4253, 4423, 9689, 9941, 11213, 19937, 21701, 23209, 44497, 86243, 110503, 132049, 216091, 756839, 859433, 1257787, 1398269, 2976221, 3021377, 6972593, 13466917, 20996011, 24036583, 25964951, 30402457, 32582657};

%t lst = {}; maxk = 5000; maxn = 15;

%t For[n = 1, n ≤ maxn, n++,

%t For[k = 0, k ≤ maxk, k++,

%t If[PrimeQ[k*(2^(2*A000043[[n]]) - 1) + 1], AppendTo[lst, k]; Break[]]

%t ]

%t ];

%t lst (* _Robert Price_, Apr 05 2016 *)

%Y Cf. A000043.

%K nonn,more

%O 1,1

%A _Pierre CAMI_, Jan 28 2016

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Last modified August 15 00:19 EDT 2024. Contains 375171 sequences. (Running on oeis4.)