A174862
Smallest prime p such that the sum of the squares of primes up to p is a multiple of 10^n.
Original entry on oeis.org
907, 977, 977, 36643, 1067749, 17777197, 71622461, 2389799983, 31252968359, 49460594569, 1915014433303, 4076200167673
Offset: 1
For a(1) = 907, 2^2 + 3^2 + 5^2 + ... + 907^2 = 37464550, which is a multiple of 10^1.
For a(2) = 977, 2^2 + ... + 977^2 = 46403000, which is a multiple of 10^2 and 10^3.
A330309
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.
Original entry on oeis.org
11, 751, 1129, 361649, 361649, 12462809, 12462809, 1273183931, 1273183931, 671946598957, 1936133384597
Offset: 1
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.
- Charles R Greathouse IV and others, Sums of Squares, thread in Mersenneforum, December 2010.
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for(n=1,4,my(n10=10^n,s=0);forprime(p=2,oo,s+=p^p;if(!(s%n10),print1(p,", ");break)))
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