A255314 Prime numbers of the form k*(k+1) + (k*(k+1))^2 + 1.

7, 43, 157, 421, 8191, 12211, 74257, 117307, 660157, 985057, 1588861, 2435161, 3263443, 4676407, 6004951, 8193907, 12535141, 18408391, 20761693, 27630793, 34251757, 36078043, 55987807, 79753831, 94138507, 106141507, 119257321, 197191807, 217931407, 225195043, 281249671, 357455743

Offset

1,1

Comments

These prime numbers are of the form A002378(k) + A002378(k)^2 + 1.

Also, prime numbers of the form 1 + k + 2*k^2 + 2*k^3 + k^4. - Wesley Ivan Hurt, Feb 21 2015

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

7 is a term since k=1 gives 1*2 + (1*2)^2 + 1 = 7, which is prime.

Maple

A255314:=n->`if`(isprime(1+n+2*n^2+2*n^3+n^4), 1+n+2*n^2+2*n^3+n^4, NULL): seq(A255314(n), n=1..200); # Wesley Ivan Hurt, Feb 28 2015

Mathematica

Select[Table[(n+1) n + ((n+1) n)^2 + 1, {n, 200}], PrimeQ]

Prog

(PARI) for(n=1, 100, if(isprime(p=1+n+2*n^2+2*n^3+n^4), print1(p, ", "))) \\ Derek Orr, Feb 28 2015
(Magma) [a: n in [0..150] | IsPrime(a) where a is n*(n + 1) + (n*(n + 1))^2 + 1 ]; // Vincenzo Librandi, Mar 24 2015

Crossrefs

Cf. A002378.

Sequence in context: A114352 A201707 A365302 * A166813 A112563 A143569

Adjacent sequences: A255311 A255312 A255313 * A255315 A255316 A255317

Keyword

nonn

Author

Waldemar Puszkarz, Feb 20 2015

Status

approved