

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.


2



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

1,1


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).


LINKS

Table of n, a(n) for n=1..11.
Charles R Greathouse IV and others, Sums of Squares, thread in Mersenneforum, December 2010.


EXAMPLE

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.


PROG

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


CROSSREFS

Cf. A174106, A174862, A330308.
Sequence in context: A206646 A267908 A180740 * A110776 A058392 A100369
Adjacent sequences: A330306 A330307 A330308 * A330310 A330311 A330312


KEYWORD

nonn,more,hard


AUTHOR

Hugo Pfoertner, Dec 10 2019


EXTENSIONS

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


STATUS

approved



