A073826 - OEIS

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A073826

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

5, 3413, 50069, 10405071317, 208492413443704093346554910065262730566475781

(list; graph; refs; listen; history; text; internal format)

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.

LINKS

Table of n, a(n) for n=1..5.

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

Adjacent sequences: A073823 A073824 A073825 * A073827 A073828 A073829

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