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.

11, 751, 1129, 361649, 361649, 12462809, 12462809, 1273183931, 1273183931, 671946598957, 1936133384597

Offset: 1

Author

Hugo Pfoertner, Dec 10 2019

Keywords

• nonn
• more
• hard

Comments

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).

Examples

			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.
		

Links

• Charles R Greathouse IV and others, Sums of Squares, thread in Mersenneforum, December 2010.

Crossrefs

Cf. A174106, A174862, A330308.

Programs

PARI

for(n=1,4,my(n10=10^n,s=0);forprime(p=2,oo,s+=p^p;if(!(s%n10),print1(p,", ");break)))

Extensions

a(10)-a(11) from Giovanni Resta, Dec 11 2019