%I #54 Apr 13 2020 15:34:00
%S 3,701,45269999
%N Primes of the form Sum_{k=1..n} k^(k-1).
%C Searched up to n = 5000.
%C a(4) has 38019 digits (1973212031 ... 7493445627) and corresponds to n=9553. - _Robert Price_, Sep 23 2016; [number of digits in a(4) corrected by _Jon E. Schoenfield_, Nov 06 2016]
%C No other primes corresponding to n < 80000. - _Robert Price_, Mar 17 2017
%H Sebastiao Antonio da Silva, <a href="https://primes.utm.edu/curios/page.php/9.html">Prime Curios: 9^8 + 8^7 + 7^6 + 6^5 + 5^4 + 4^3 + 3^2 + 2^1 + 1^0 is prime</a>
%e 3 is in the sequence because 3 is prime and 3 = 2^1 + 1^0.
%e 701 is in the sequence because 701 is prime and 701 = 5^4 + 4^3 + 3^2 + 2^1 + 1^0.
%e 45269999 is in the sequence because 45269999 is prime and 45269999 = 9^8 + 8^7 + 7^6 + 6^5 + 5^4 + 4^3 + 3^2 + 2^1 + 1^0.
%t Select[Accumulate[Table[n^(n-1),{n,100}]],PrimeQ] (* _Harvey P. Dale_, Apr 13 2020 *)
%o (Sage)
%o sum = 0
%o seq = []
%o max_n = 2500
%o for n in range(1, max_n+1):
%o sum += n^(n-1)
%o if is_prime(sum):
%o seq.append(n)
%o print(seq)
%Y Primes in A060946.
%K nonn,bref
%O 1,1
%A _Robert C. Lyons_, Sep 06 2016
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