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A073825
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Numbers n such that Sum k^k, k=1..n, is prime.
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5
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OFFSET
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1,1
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COMMENTS
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For every n, a(n) must be equal to 1 or 2 (mod 4) because Sum[k^k,{k,a(n)}] must be odd. Any additional terms are greater than 5368 with the next prime having more than 20025 digits. - Farideh Firoozbakht, Aug 09 2003
Soundararajan finds an asymptotic upper bound of log k / log log k prime numbers of the form 1^1 + 2^2 + ... + n^n less than k; that is, n << log a(n) / log log a(n). - Charles R Greathouse IV, Aug 27 2008
According to Andersen, the next term is larger than 28000, cf. link. [From M. F. Hasler, Mar 01 2009]
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REFERENCES
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K. Soundararajan, "Primes in a Sparse Sequence", Journal of Number Theory 43:2 (1993), pp. 220-227.
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LINKS
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Table of n, a(n) for n=1..5.
C. Rivera, Prime puzzle #404. [From M. F. Hasler, Mar 01 2009]
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MAPLE
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List073825:=proc(q) local a, n; a:=0;
for n from 1 to q do a:=a+n^n; if isprime(a) then print(n); fi; od; end:
List073825(100); # Paolo P. Lava, Apr 10 2013
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MATHEMATICA
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v={}; Do[If[(Mod[n, 4]==1||Mod[n, 4]==2)&&PrimeQ[Sum[k^k, {k, n}]], v=Insert[v, n, -1]; Print[v]], {n, 5368}]
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PROG
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(PARI) s=0; for(k=1, 1320, s=s+k^k; if(isprime(s), print1(k, ", ")))
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CROSSREFS
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Cf. A073826 (corresponding primes), A001923 (Sum k^k, k=1..n).
Sequence in context: A057250 A056643 A057256 * A015891 A160645 A206332
Adjacent sequences: A073822 A073823 A073824 * A073826 A073827 A073828
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KEYWORD
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nonn,changed
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AUTHOR
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Rick L. Shepherd, Aug 13 2002
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EXTENSIONS
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Any additional terms are greater than 1320 with the next prime having more than 4120 digits.
No terms out to 3000. The next term would yield a prime with over 10000 digits. - John Sillcox (johnsillcox(AT)hotmail.com), Aug 05 2003
Edited by Charles R Greathouse IV, Oct 27 2010
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STATUS
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approved
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