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A073826
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Primes of the form sum( k^k, k=1..n), i.e. primes in A001923.
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4
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OFFSET
| 1,1
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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.
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FORMULA
| a(j) = A001923(A073825(j)) = sum( k^k, k=1..A073825(j)).
A073826 = intersection of A001923 with A000040.
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EXAMPLE
| 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).
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MATHEMATICA
| Select[s=0; Table[s+=n^n, {n, 5!}], PrimeQ[ # ]&] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), May 30 2010]
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PROG
| (PARI) s=0; for(k=1, 1320, s=s+k^k; if(isprime(s), print1(s, ", ")))
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CROSSREFS
| 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: A204940 A172954 A079173 * A159397 A024074 A086896
Adjacent sequences: A073823 A073824 A073825 * A073827 A073828 A073829
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 13 2002
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EXTENSIONS
| Edited by M. F. Hasler (www.univ-ag.fr/~mhasler), Mar 22 2008
Typo in comment corrected by Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 23 2008
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