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A221207 Primes of the form 2^(n-2)*(n+2)^2 + 1. 0

%I

%S 2,17,2593,5308417,26214401,57802753,584652423169,5566277615617,

%T 24807731101697,2128654511374337,114923510727115685920505857,

%U 626707144888223764167681638401,28901765777295687591430290881352276511750619137

%N Primes of the form 2^(n-2)*(n+2)^2 + 1.

%C Generated by n: 0, 2, 7, 16, 18, 19, 31, 34, 36, 42, 76, 88, ... ; primes in this sequence of n are 2, 7, 19, 31, ...

%C Two sub-aspects: Smallest nonnegative k such that 2^(k-2)*(n+ 2)^2 + 1 is prime, for n >= 0: 0, 3, 0, 4, 1, 4, 0, 3, 2, 10, 0, 4, 2, 5, 2, 12, 1, 30, 0, 3, 8, ...

%C Smallest nonnegative k such that 2^(n-2)*(k+2)^2 + 1 is prime, for n >= 0: 0, 0, 0, 1, 0, 1, 2, 4, 0, 1, 8, 4, 3, 1, 2, 10, 0, 4, 7, 1, 8, ...

%C Further terms, for n equal to 142, 208, 288, 582, 2017, 2100, ..., have 47, 67, 92, 181, 614, 639, ... digits. - _Paolo P. Lava_, Apr 04 2013

%e a(0) = 2 = 2^(0-2)*(0+2)^2 + 1 = (1/4) * 4 + 1.

%p List221207:=proc(q) local n; lprint(0,2);

%p for n from 2 to q do

%p if isprime(2^(n-2)*(n+2)^2+1) then lprint(n,2^(n-2)*(n+2)^2+1);

%p fi; od; end:

%p List221207(2100); # _Paolo P. Lava_, Apr 04 2013

%t Select[Table[2^(n - 2)*(n + 2)^2 + 1, {n, 0, 200}], PrimeQ] (* _T. D. Noe_, Apr 05 2013 *)

%o (PARI) for(n=0,1e3,is(ispseudoprime(t=2^(n-2)*(n + 2)^2+1), print1(t", "))) \\ _Charles R Greathouse IV_, Mar 18 2014

%K nonn,less

%O 1,1

%A _Irina Gerasimova_, Feb 21 2013

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Last modified June 16 21:20 EDT 2019. Contains 324155 sequences. (Running on oeis4.)