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Prime numbers p such that the sum of the first p odd primes is divisible by p.
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%I #20 Sep 30 2016 09:49:31

%S 2,3,73,3420839

%N Prime numbers p such that the sum of the first p odd primes is divisible by p.

%C Primes in A097961. - _Altug Alkan_, Aug 24 2016

%C a(5) > 10^10. - _Dana Jacobsen_, Sep 29 2016

%e a(2) = 3 since 3+5+7 = 15 is divisible by the prime number 3.

%o (PARI) a071148(n) = sum(k=2, n+1, prime(k))

%o isdivisible(n) = Mod(a071148(n), n)==0

%o terms(n) = my(i=0, p=2); while(i < n, if(isdivisible(p), print1(p, ", "); i++); p=nextprime(p+1))

%o /* The following function call prints the initial four terms */

%o terms(4) \\ _Felix Fröhlich_, Aug 24 2016

%o (Perl) use ntheory ":all"; my($s,$l,$pr)=(0,0,prime_iterator(3)); forprimes { $s += $pr->() for $l+1 .. $_; $l=$_; say unless $s % $_; } 1e7; # _Dana Jacobsen_, Sep 23 2016

%Y Cf. A071148, A097961.

%K nonn,hard,more

%O 1,1

%A _G. L. Honaker, Jr._, Aug 24 2016