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Smallest prime p such that the sum of the squares of primes up to p is a multiple of 10^n.
2

%I #13 Dec 11 2019 17:03:23

%S 907,977,977,36643,1067749,17777197,71622461,2389799983,31252968359,

%T 49460594569,1915014433303,4076200167673

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

%C Sequence discovery attributed to davar55. Initial work performed by _Charles R Greathouse IV_. Sequence extension performed and custom software written by _Benjamin R. Buhrow_.

%H Mersenneforum, <a href="http://www.mersenneforum.org/showthread.php?t=13181">Sums of Squares</a> puzzle, Mar 18 2010.

%H Ben Buhrow, <a href="http://sites.google.com/site/bbuhrow/home/sums-of-prime-squares">Software and extended tables.</a>

%e For a(1) = 907, 2^2 + 3^2 + 5^2 + ... + 907^2 = 37464550, which is a multiple of 10^1.

%e For a(2) = 977, 2^2 + ... + 977^2 = 46403000, which is a multiple of 10^2 and 10^3.

%Y Cf. A330308, A330309.

%K nonn,more,hard

%O 1,1

%A _Benjamin R. Buhrow_, Mar 31 2010