A188269 - OEIS

%I #46 Sep 21 2024 19:26:00

%S 5,59,348077,10023053,30414227,55367063,72452489,85856933,109346759,

%T 182679473,254112143,305966369,433051637,727914497,2029672529,

%U 4178961167,6528621257,8346080159,12783893813,17220494579,17993776223,19618171127,23673478589,29448235247,43333033853

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

%C Bunyakovsky's conjecture implies that this sequence is infinite. - _Charles R Greathouse IV_, Jun 09 2011

%C All the terms in the sequence are congruent to 2 mod 3. - _K. D. Bajpai_, Apr 11 2014

%H Charles R Greathouse IV, <a href="/A188269/b188269.txt">Table of n, a(n) for n = 1..10000</a>

%e 5 is prime and appears in the sequence because 0^4 + 1^3 + 2^2 = 5.

%e 59 is prime and appears in the sequence because 2^4 + 3^3 + 4^2 = 59.

%e 348077 = 24^4 + (24+1)^3 + (24+2)^2 = 24^4 + 25^3 + 26^2.

%e 10023053 = 56^4 + (56+1)^3 + (56+2)^2 = 56^4 + 57^3 + 58^2.

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

%t lst={};Do[If[PrimeQ[p=n^4+n^3+4*n^2+7*n+5], AppendTo[lst, p]],{n,200}];lst

%t Select[Table[n^4+n^3+4n^2+7n+5,{n,500}],PrimeQ] (* _Harvey P. Dale_, Jun 19 2011 *)

%o (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

%Y Cf. A088548, A088550, A156018.

%K nonn

%O 1,1

%A _Rafael Parra Machio_, Jun 09 2011

%E Duplicate Mathematica program deleted by _Harvey P. Dale_, Jun 19 2011

%E Missing term 5 inserted by _Alois P. Heinz_, Sep 21 2024