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A221207 Primes of the form 2^(n-2)*(n+2)^2 + 1. 0
2, 17, 2593, 5308417, 26214401, 57802753, 584652423169, 5566277615617, 24807731101697, 2128654511374337, 114923510727115685920505857, 626707144888223764167681638401, 28901765777295687591430290881352276511750619137 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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, ...

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, ...

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, ...

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

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

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

MAPLE

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

for n from 2 to q do

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

fi; od;  end:

List221207(2100); # Paolo P. Lava, Apr 04 2013

MATHEMATICA

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

PROG

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

CROSSREFS

Sequence in context: A284706 A092415 A274053 * A274015 A279884 A060353

Adjacent sequences:  A221204 A221205 A221206 * A221208 A221209 A221210

KEYWORD

nonn,less

AUTHOR

Irina Gerasimova, Feb 21 2013

STATUS

approved

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Last modified May 19 14:36 EDT 2019. Contains 323395 sequences. (Running on oeis4.)