A354831 - OEIS

%I #17 Jul 22 2022 10:38:37

%S 5,373,46309,6732373,26450599458469,4317810550653973,

%T 15647143198792684919908583741989,

%U 6864681654384231304317569259724531213945845885866391974437116993829,5599548608682504162062596274137068329320798013420534505888549721133699842789

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

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

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

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

%o (Python)

%o from sympy import isprime

%o from itertools import count, islice

%o 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))

%o print(list(islice(agen(), 9))) # _Michael S. Branicky_, Jun 07 2022

%Y A352393 gives the corresponding exponents.

%Y Cf. A166241.

%K nonn

%O 1,1

%A _Hemjyoti Nath_, Jun 07 2022