

A056561


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


23



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
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OFFSET

1,3


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


REFERENCES

P. Hoffman, Archimedes' Revenge, pp. 3940,Penguin Books 1988.


LINKS

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


FORMULA

a(n) = (sqrt(4*A005846(n)163)1)/2.
a(n) = A002837(n+1)1.  Robert Price, Nov 08 2019


EXAMPLE

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.


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 *)


PROG

(MAGMA) [n: n in [0..80] IsPrime(n^2 + n + 41)]; // Vincenzo Librandi, Sep 28 2012
(Haskell)
a056561 n = a056561_list !! (n1)
a056561_list = filter ((== 1) . a010051' . a202018) [0..]
 Reinhard Zumkeller, Jul 03 2015
(PARI) is(n)=isprime(n^2+n+41) \\ Charles R Greathouse IV, Sep 02 2015


CROSSREFS

Cf. A002837, A005846, A007634, A010051, A202018, A259645.
Sequence in context: A083243 A002837 A271143 * A321993 A236674 A273886
Adjacent sequences: A056558 A056559 A056560 * A056562 A056563 A056564


KEYWORD

nonn,easy


AUTHOR

Henry Bottomley, Jun 26 2000


STATUS

approved



