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

1,1

Comments

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).

Links

Table of n, a(n) for n=1..12.

Ben Buhrow, Software and extended tables, 07 Apr 2010.

Ben Buhrow and others, Sums of Squares, thread in Mersenneforum, April 2010.

Example

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.

Prog

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

Crossrefs

Cf. A174106, A174862, A330309.

Sequence in context: A176898 A274996 A142668 * A157710 A265957 A137085

Adjacent sequences: A330305 A330306 A330307 * A330309 A330310 A330311

Keyword

nonn,more,hard

Author

Hugo Pfoertner, Dec 10 2019

Status

approved