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URL: https://oeis.org/A187602

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A187602
Primes of the form (k+1)^(k-1) + k.
2
2, 5, 19, 1301, 262151, 4782977
OFFSET
1,1
COMMENTS
The next terms are too large to be displayed:
a(7) = 159^157 + 158 (k = 158), which is 346 digits long.
a(8) = 537^535 + 536 (k = 536), which is 1461 digits long.
a(9) = 4671^4669 + 4670 (k = 4670), which is 17133 digits long.
a(10) = 9796^9794 + 9795 (k = 9795), which is 39089 digits long.
Next term has k >= 30000.
EXAMPLE
1301 is in the sequence since it is prime and, using k = 5, (k+1)^(k-1) + k = 6^4 + 5 = 1296 + 5 = 1301.
MATHEMATICA
Do[p=(n+1)^(n-1)+n; If[PrimeQ[p], Print[p]], {n, 250}]
Select[Table[(n+1)^(n-1)+n, {n, 20}], PrimeQ] (* Harvey P. Dale, Oct 17 2025 *)
PROG
(PARI) lista(nn) = for(k=1, nn, if(ispseudoprime(q=(k+1)^(k-1)+k), print1(q, ", "))); \\ Jinyuan Wang, Mar 01 2020
CROSSREFS
Cf. A238378 (corresponding k).
Sequence in context: A269997 A270547 A177875 * A260140 A270556 A059079
KEYWORD
nonn,hard
AUTHOR
Marco Ripà, Mar 11 2011
EXTENSIONS
a(8)-a(10) from Matevz Markovic, Mar 03 2014
STATUS
approved