A174106 -id:A174106 - cp's OEIS frontend

A330308 Smallest prime p such that the sum of cubes of all primes up to p is a multiple of 10^n.

5, 233, 8783, 24763, 5828099, 9229931, 262707241, 7717488553, 34529828929, 311995561321, 549120448879, 33777547344991

Offset: 1

Hugo Pfoertner, Dec 10 2019

Suggested in a discussion in Mersenneforum, with contributions by users "davar55", Charles R Greathouse IV, and Benjamin R. Buhrow. The latter calculated terms a(1)-a(12) of this sequence (see links).

			a(1): 10 divides prime cube sum up to 5, sum = 2^3 + 3^3 + 5^3 = 160;
a(2): 100 divides prime cube sum up to 233, sum = 143309500;
a(3): 1000 divides prime cube sum up to 8783, sum = 167992435025000.

Ben Buhrow, Software and extended tables, 07 Apr 2010.
Ben Buhrow and others, Sums of Squares, thread in Mersenneforum, April 2010.

Cf. A174106, A174862, A330309.

for(n=1,8,my(n10=10^n,s=0);forprime(p=2,oo,s+=p^3;if(!(s%n10),print1(p,", ");break)))

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

Hugo Pfoertner, Dec 10 2019

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).

			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.

Cf. A174106, A174862, A330308.

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

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

cp's OEIS Frontend

A330308 Smallest prime p such that the sum of cubes of all primes up to p is a multiple of 10^n.

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