A123129 a(n) = ( n + prime(n+1) - prime(n) )^(n-1).

1, 4, 25, 512, 2401, 100000, 531441, 35831808, 2562890625, 5159780352, 2015993900449, 17592186044416, 129746337890625, 20822964865671168, 3243919932521508681, 136880068015412051968, 288441413567621167681

Offset: 1

Author

Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 30 2006

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..350
• Sergio Silva, Teste Numerico.

Crossrefs

Cf. A000040, A001223, A014690, A095116.

Programs

Mathematica

Table[(n +Prime[n+1] -Prime[n])^(n-1), {n, 1, 30}] (* G. C. Greubel, Aug 04 2021 *)

PARI

for(n=1, 25, print1( (prime(n+1) -prime(n) +n)^(n-1), ","))

Sage

[(n + nth_prime(n+1) - nth_prime(n))^(n-1) for n in (1..30)] # G. C. Greubel, Aug 04 2021

Formula

a(n) = ( n + prime(n+1) - prime(n) )^(n-1) = ( n + A001223(n) )^(n-1).

From G. C. Greubel, Aug 04 2021: (Start)

a(n) = (A014690(n) - prime(n))^(n-1) = (A095116(n+1) - prime(n))^(n-1).

a(n) = (prime(n+1) - A014689(n))^(n-1). (End)