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A180475 Primes of the form p^5 + p^3 + 1 where p is a prime. 1
41, 271, 3251, 1424771, 6448511, 115925123, 229448831, 18425794691, 38581737743, 48264295811, 73443083699, 996266439503, 1258302388991, 1752012093443, 2159450038451, 2909420102783, 3201110256371, 18248780996099, 32198944966271, 124287677598479, 142214634995891 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Michael S. Branicky, Table of n, a(n) for n = 1..10000

FORMULA

a(n) ~ prime(n)^18.

EXAMPLE

115925123 is a term since 41^5 + 41^3 + 1 = 115925123 is prime.

MATHEMATICA

Select[ #^5 + #^3 + 1 & /@ Prime@ Range@ 90, PrimeQ] (* Robert G. Wilson v, Sep 10 2010 *)

PROG

(Python)

from itertools import islice

from sympy import isprime, nextprime

def agen(): # generator of terms

    p = 2

    while True:

        t = p**5 + p**3 + 1

        if isprime(t):

            yield t

        p = nextprime(p)

print(list(islice(agen(), 21))) # Michael S. Branicky, Mar 12 2022

CROSSREFS

Cf. A000040, A180474.

Sequence in context: A020866 A142690 A089318 * A142768 A140013 A342299

Adjacent sequences:  A180472 A180473 A180474 * A180476 A180477 A180478

KEYWORD

nonn

AUTHOR

Carmine Suriano, Sep 07 2010

EXTENSIONS

a(19) and beyond from Michael S. Branicky, Mar 12 2022

STATUS

approved

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Last modified May 27 11:47 EDT 2022. Contains 354097 sequences. (Running on oeis4.)