A330309 -id:A330309 - cp's OEIS frontend

A174862 Smallest prime p such that the sum of the squares of primes up to p is a multiple of 10^n.

907, 977, 977, 36643, 1067749, 17777197, 71622461, 2389799983, 31252968359, 49460594569, 1915014433303, 4076200167673

Offset: 1

Benjamin R. Buhrow, Mar 31 2010

Sequence discovery attributed to davar55. Initial work performed by Charles R Greathouse IV. Sequence extension performed and custom software written by Benjamin R. Buhrow.

			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.

Mersenneforum, Sums of Squares puzzle, Mar 18 2010.
Ben Buhrow, Software and extended tables.

Cf. A330308, A330309.

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

Original entry on oeis.org

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)))

cp's OEIS Frontend

A174862 Smallest prime p such that the sum of the squares of primes up to p is a multiple of 10^n.

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