A123113 Main diagonal of prime power sum array.

2, 13, 280, 17489, 48909526, 13423779037, 232729381165100, 146367546237420097, 8864305651125125485354, 100000100010100010100010101101, 193529735150413879906083607547512

Offset

1,1

Comments

Main diagonal of the infinite array T(k,n) = 1 + Sum_{i=1..k} n^prime(i).

a(n) is prime for n = 1, 2, 4 -- what is the next prime in the sequence?

The next prime in the sequence is for n = 20. It has 93 digits. - Harvey P. Dale, Jan 18 2017

Links

G. C. Greubel, Table of n, a(n) for n = 1..75

Formula

a(n) = 1 + n^2 + n^3 + n^5 + ... + n^prime(n).

Example

a(1) = 2 = 1 + 1^2.
a(2) = 13 = 1 +2^2 +2^3.
a(3) = 280 = 1 +3^2 +3^3 +3^5.
a(4) = 17489 = 1 +4^2 +4^3 +4^5 +4^7.
a(5) = 48909526 = 1 +5^2 +5^3 +5^5 +5^7 +5^11.
a(6) = 13423779037 = 1 +6^2 +6^3 +6^5 +6^7 +6^11 +6^13.
a(7) = 232729381165100 = 1 +7^2 +7^3 +7^5 +7^7 +7^11 +7^13 +7^17.
a(8) = 146367546237420097 = 1 +8^2 +8^3 +8^5 +8^7 +8^11 +8^13 +8^17 +8^19.

Mathematica

Table[Total[n^Prime[Range[n]]]+1, {n, 15}] (* Harvey P. Dale, Jan 18 2017 *)

Prog

(Magma) [1 + (&+[n^NthPrime(j): j in [1..n]]): n in [1..15]]; // G. C. Greubel, Jul 21 2021
(Sage) [1 + sum(n^nth_prime(j) for j in (1..n)) for n in (1..15)] # G. C. Greubel, Jul 21 2021

Crossrefs

Cf. A000040, A062481.

Sequence in context: A356493 A334089 A326360 * A126742 A013051 A351022

Adjacent sequences: A123110 A123111 A123112 * A123114 A123115 A123116

Keyword

easy,nonn

Author

Jonathan Vos Post, Sep 28 2006

Status

approved