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A255314 Prime numbers of the form n*(n + 1) + (n*(n + 1))^2 + 1. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..32.

EXAMPLE

7 is a term since n=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: A183537 A114352 A201707 * A166813 A112563 A143569

Adjacent sequences:  A255311 A255312 A255313 * A255315 A255316 A255317

KEYWORD

nonn

AUTHOR

Waldemar Puszkarz, Feb 20 2015

STATUS

approved

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Last modified June 25 04:06 EDT 2021. Contains 345451 sequences. (Running on oeis4.)