A056561 Numbers n such that n^2 + n + 41 is prime.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 42, 43, 45, 46, 47, 48, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 78

Offset: 1

Author

Henry Bottomley, Jun 26 2000

Keywords

• nonn
• easy

Comments

Among first 100000 terms, the only run of 13 subsequent values >39 is 219..231. - Zak Seidov, Jan 28 2009

Number of terms less than 10^n: 1, 10, 86, 581, 4149, 31985, 261081, 2208197, 19132652, ... . - Robert G. Wilson v, Apr 20 2015

Complement of A007634. - Robert Israel, Apr 20 2015

Examples

			39 is in the sequence because 39^2+39+41=1601 which is prime but 40 is not because 40^2+40+41=1681=41*41.
		

References

• P. Hoffman, Archimedes' Revenge, pp. 39-40,Penguin Books 1988.

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Euler Prime

Crossrefs

Cf. A002837, A005846, A007634, A010051, A202018, A259645.

Programs

Haskell

a056561 n = a056561_list !! (n-1)
a056561_list = filter ((== 1) . a010051' . a202018) [0..]
-- Reinhard Zumkeller, Jul 03 2015

Magma

[n: n in [0..80] |IsPrime(n^2 + n + 41)]; // Vincenzo Librandi, Sep 28 2012

Maple

select(t -> isprime(t^2+t+41), [$0..100]); # Robert Israel, Apr 20 2015

Mathematica

Select[Range[80], PrimeQ[#^2 + # + 41] &] (* Vincenzo Librandi, Sep 28 2012 *)

PARI

is(n)=isprime(n^2+n+41) \\ Charles R Greathouse IV, Sep 02 2015

Formula

a(n) = (sqrt(4*A005846(n)-163)-1)/2.

a(n) = A002837(n+1)-1. - Robert Price, Nov 08 2019