A155933 Primes of the form n^2 + (n+1)^3.

31, 73, 241, 379, 2341, 3571, 6121, 9661, 20359, 47881, 51949, 60763, 65521, 119953, 135151, 291721, 305119, 378289, 394201, 427351, 537841, 689041, 736921, 761671, 921889, 1202041, 1271161, 1306693, 1494313, 1533871, 1742161, 1785961, 1875751

Offset

1,1

Comments

For n^2 + (n+1)^3 to be a prime, n cannot be 1 modulo 3 whereas all a(n) are definitely 1 modulo 3. - Avik Roy (avik_3.1416(AT)yahoo.co.in), Feb 13 2009

Links

Zak Seidov, Table of n, a(n) for n = 1..2000

Formula

a(n) = m^2 + (m+1)^3 where m = A128958(n). - Zak Seidov, Dec 15 2013

Example

31 is in the sequence since 31 is prime and 31 = 2^2 + 3^3.

Mathematica

lst={}; Do[p=(n+2)^2+(n+3)^3; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 2*5!}]; lst...and/or...lst={}; Do[p=n^2+(n+1)^3; If[PrimeQ[p], AppendTo[lst, p]], {n, 0, 2*5!}]; lst

Crossrefs

Cf. A128958.

Sequence in context: A070954 A141892 A298613 * A163428 A130468 A068917

Adjacent sequences: A155930 A155931 A155932 * A155934 A155935 A155936

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Jan 30 2009

Extensions

Definition corrected by Zak Seidov, Jul 05 2013

Status

approved