login
A073826
Primes of the form Sum_{k=1..n} k^k, i.e., primes in A001923.
6
5, 3413, 50069, 10405071317, 208492413443704093346554910065262730566475781
OFFSET
1,1
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.
FORMULA
a(j) = A001923(A073825(j)) = sum_{k=1..A073825(j)} k^k.
Intersection of A001923 with A000040.
EXAMPLE
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).
MATHEMATICA
Select[s=0; Table[s+=n^n, {n, 5!}], PrimeQ[ # ]&] (* Vladimir Joseph Stephan Orlovsky, May 30 2010 *)
PROG
(PARI) s=0; for(k=1, 1320, s=s+k^k; if(isprime(s), print1(s, ", ")))
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)).
Sequence in context: A204940 A172954 A079173 * A159397 A024074 A276238
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Aug 13 2002
EXTENSIONS
Edited by M. F. Hasler, Mar 22 2008
Typo in comment corrected by Jonathan Vos Post, Mar 23 2008
STATUS
approved