1,1

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.

a(j) = A001923(A073825(j)) = sum( k^k, k=1..A073825(j)).

A073826 = intersection of A001923 with A000040.

a(1) = 5 = 1^1+2^2 is the smallest prime of the form A001923(n) = sum( k^k, k=1..n), namely for n = 2 = A073825(1).

a(2) = sum( k^k, k=1..A073825(2)) = 1^1 + 2^2 + 3^3 + 4^4 + 5^5 = 3413, a prime, so 3413 is in this sequence (A073825(2) = 5).

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

Cf. A073825 (corresponding n), A001923 (sum( k^k, k=1..n)).

Cf. A122166: indices of primes in A062970 (sum( k^k, k=0..n)).

Sequence in context: A013782 A137841 A079173 this_sequence A159397 A024074 A086896

Adjacent sequences: A073823 A073824 A073825 this_sequence A073827 A073828 A073829

nonn

Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 13 2002

Edited by M. F. Hasler (MHasler(AT)univ-ag.fr), Mar 22 2008

Typo in comment corrected by Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 23 2008