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 A073825 Numbers n such that Sum k^k, k=1..n, is prime. 5
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 OFFSET 1,1 COMMENTS 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] REFERENCES K. Soundararajan, "Primes in a Sparse Sequence", Journal of Number Theory 43:2 (1993), pp. 220-227. LINKS C. Rivera, Prime puzzle #404. [From M. F. Hasler, Mar 01 2009] MAPLE 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 MATHEMATICA 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}] PROG (PARI) s=0; for(k=1, 1320, s=s+k^k; if(isprime(s), print1(k, ", "))) CROSSREFS 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 KEYWORD nonn,changed AUTHOR Rick L. Shepherd, Aug 13 2002 EXTENSIONS 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 STATUS approved

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