A188269 Prime numbers of the form k^4 + k^3 + 4*k^2 + 7*k + 5 = k^4 + (k+1)^3 + (k+2)^2.

5, 59, 348077, 10023053, 30414227, 55367063, 72452489, 85856933, 109346759, 182679473, 254112143, 305966369, 433051637, 727914497, 2029672529, 4178961167, 6528621257, 8346080159, 12783893813, 17220494579, 17993776223, 19618171127, 23673478589, 29448235247, 43333033853

Offset: 1

Author

Rafael Parra Machio, Jun 09 2011

Keywords

• nonn

Comments

Bunyakovsky's conjecture implies that this sequence is infinite. - Charles R Greathouse IV, Jun 09 2011

All the terms in the sequence are congruent to 2 mod 3. - K. D. Bajpai, Apr 11 2014

Examples

			5 is prime and appears in the sequence because 0^4 + 1^3 + 2^2 = 5.
59 is prime and appears in the sequence because 2^4 + 3^3 + 4^2 = 59.
348077 = 24^4 + (24+1)^3 + (24+2)^2 = 24^4 + 25^3 + 26^2.
10023053 = 56^4 + (56+1)^3 + (56+2)^2 = 56^4 + 57^3 + 58^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088548, A088550, A156018.

Programs

Maple

select(isprime, [n^4+(n+1)^3+(n+2)^2$n=0..1000])[]; # K. D. Bajpai, Apr 11 2014

Mathematica

lst={};Do[If[PrimeQ[p=n^4+n^3+4*n^2+7*n+5], AppendTo[lst, p]],{n,200}];lst
Select[Table[n^4+n^3+4n^2+7n+5,{n,500}],PrimeQ] (* Harvey P. Dale, Jun 19 2011 *)

PARI

for(n=1,1e3,if(isprime(k=n^4+n^3+4*n^2+7*n+5),print1(k", "))) \\ Charles R Greathouse IV, Jun 09 2011

Extensions

Duplicate Mathematica program deleted by Harvey P. Dale, Jun 19 2011

Missing term 5 inserted by Alois P. Heinz, Sep 21 2024