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%I #21 Dec 12 2019 17:49:48
%S 11,751,1129,361649,361649,12462809,12462809,1273183931,1273183931,
%T 671946598957,1936133384597
%N Smallest prime p such that the sum of all powers of primes 2^2 + 3^3 + ... + p^p up to p is a multiple of 10^n.
%C Suggested in a discussion in Mersenneforum, with contributions by users (among others) "davar55", _Benjamin R. Buhrow_, and _Charles R Greathouse IV_. The latter calculated the terms a(1)-a(9) of this sequence (see link).
%H Charles R Greathouse IV and others, <a href="https://www.mersenneforum.org/showthread.php?t=13181&page=11">Sums of Squares</a>, thread in Mersenneforum, December 2010.
%e a(1) = 11: 2^2 = 4, 2^2 + 3^3 = 31, 2^2 + 3^3 + 5^5 = 3156, 2^2 + 3^3 + 5^5 + 7^7 = 826699, 2^2 + 3^3 + 5^5 + 7^7 + 11^11 = 285312497310 -> smallest sum divisible by 10^1.
%o (PARI) for(n=1,4,my(n10=10^n,s=0);forprime(p=2,oo,s+=p^p;if(!(s%n10),print1(p,", ");break)))
%Y Cf. A174106, A174862, A330308.
%K nonn,more,hard
%O 1,1
%A _Hugo Pfoertner_, Dec 10 2019
%E a(10)-a(11) from _Giovanni Resta_, Dec 11 2019
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