A354831 Primes of the form 3^k + 5^k + 7^k + 11^k + 13^k.

5, 373, 46309, 6732373, 26450599458469, 4317810550653973, 15647143198792684919908583741989, 6864681654384231304317569259724531213945845885866391974437116993829, 5599548608682504162062596274137068329320798013420534505888549721133699842789

Offset

1,1

Links

Table of n, a(n) for n=1..9.

Example

3^2 + 5^2 + 7^2 + 11^2 + 13^2 = 373, which is a prime.
3^4 + 5^4 + 7^4 + 11^4 + 13^4 = 46309, which is a prime.

Mathematica

Select[Table[3^n + 5^n + 7^n + 11^n + 13^n, {n, 0, 1000}], PrimeQ]

Prog

(Python)
from sympy import isprime
from itertools import count, islice
def agen(): yield from (p for p in (3**k + 5**k + 7**k + 11**k + 13**k for k in count(0)) if isprime(p))
print(list(islice(agen(), 9))) # Michael S. Branicky, Jun 07 2022

Crossrefs

A352393 gives the corresponding exponents.

Cf. A166241.

Sequence in context: A160193 A215437 A098038 * A072172 A278364 A214008

Adjacent sequences: A354828 A354829 A354830 * A354832 A354833 A354834

Keyword

nonn

Author

Hemjyoti Nath, Jun 07 2022

Status

approved