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A166852 Numbers n such that n^n + 3 is prime. 4
2, 1036, 2770 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers corresponding to a(2) and a(3) are probable primes. 2770 is in the sequence so 2770^2770 + 3 is a probable prime; it is interesting that 277027703 is also prime. For the first term we have the same property: both 2^2 + 3 and 223 are prime.

The prime corresponding to the next term, if it exists, has more than 20000 digits.

For n = -1, n^n + 3 = 2 is prime but sequence focuses on the positive values of n. - Altug Alkan, Nov 28 2015

LINKS

Table of n, a(n) for n=1..3.

MATHEMATICA

Do[If[GCD[n, 3]==1&&PrimeQ[n^n+3], Print[n]], {n, 2, 5362, 2}]

PROG

(PARI) is(n)=ispseudoprime(n^n+3) \\ Charles R Greathouse IV, Jun 13 2017

CROSSREFS

Cf. A087037, A100407, A100408, A166853.

Sequence in context: A196292 A182447 A218437 * A236951 A111203 A159858

Adjacent sequences:  A166849 A166850 A166851 * A166853 A166854 A166855

KEYWORD

hard,more,nonn,bref

AUTHOR

Farideh Firoozbakht, Nov 20 2009

STATUS

approved

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Last modified June 19 00:04 EDT 2021. Contains 345125 sequences. (Running on oeis4.)