A073826 Primes of the form Sum_{k=1..n} k^k, i.e., primes in A001923.

5, 3413, 50069, 10405071317, 208492413443704093346554910065262730566475781

Offset: 1

Author

Rick L. Shepherd, Aug 13 2002

Keywords

• nonn

Comments

a(3) = A001923(10) = 10405071317 and the 45-digit a(4) = A001923(30) have been certified prime with Primo. Any additional terms are too big to include here.

The next term would have over 20000 digits; see A073825 for more information and updates.

Examples

			a(1) = 5 = 1^1 + 2^2 is the smallest prime of the form A001923(n) = sum_{k=1..n} k^k, namely for n = 2 = A073825(1).
a(2) = sum_{k=1..A073825(2)} k^k = 1^1 + 2^2 + 3^3 + 4^4 + 5^5 = 3413, a prime, so 3413 is in this sequence (A073825(2) = 5).
		

Crossrefs

Cf. A073825 (corresponding n), A001923 (sum_{k=1..n} k^k).

Cf. A122166 (indices of primes in A062970 (sum_{k=0..n} k^k)).

Programs

Mathematica

Select[s=0;Table[s+=n^n,{n,5!}],PrimeQ[ # ]&] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)

PARI

s=0; for(k=1,1320, s=s+k^k; if(isprime(s), print1(s,",")))

Formula

a(j) = A001923(A073825(j)) = sum_{k=1..A073825(j)} k^k.

Intersection of A001923 with A000040.

Extensions

Edited by M. F. Hasler, Mar 22 2008

Typo in comment corrected by Jonathan Vos Post, Mar 23 2008