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%I #41 Dec 14 2017 16:28:30
%S 197,223,251,281,311,401,431,463,523,593,659,719,757,827,863,947,991,
%T 1063,1171,1753,1901,2347,2393,2647,2689,2731,2777,2819,2953,3347,
%U 3389,3533,3643,3701,3761,3821,4177,4217,4451,4493,5507,5717,5849,5927,6029
%N Primes that are the sum of 7 consecutive primes.
%H Syed Iddi Hasan, <a href="/A082246/b082246.txt">Table of n, a(n) for n = 1..10000</a>
%e 2 + 3 + 5 + 7 + 11 + 13 + 17 = 58 = 2*29
%e 3 + 5 + 7 + 11 + 13 + 17 + 19 = 75 = 3*5^2
%e 5 + 7 + 11 + 13 + 17 + 19 + 23 = 95 = 5*19
%e 7 + 11 + 13 + 17 + 19 + 23 + 29 = 119 = 7*17
%e 11 + 13 + 17 + 19 + 23 + 29 + 31 = 143 = 11*13
%e 13 + 17 + 19 + 23 + 29 + 31 + 37 = 169 = 13*13
%e 17 + 19 + 23 + 29 + 31 + 37 + 41 = 197 (prime)
%p Primes:= select(isprime, [seq(i,i=3..10000,2)]):
%p S:= ListTools:-PartialSums(Primes):
%p select(isprime,S[8..-1]-S[1..-8]); # _Robert Israel_, Dec 14 2017
%t Select[ListConvolve[{1,1,1,1,1,1,1},Prime[Range[200]]],PrimeQ] (* _Harvey P. Dale_, Jul 12 2013 *)
%t Select[Total/@Partition[Prime[Range[200]],7,1],PrimeQ] (* _Harvey P. Dale_, Jul 24 2017 *)
%o (PARI) \\ primes in the sum of m odd number of consecutive primes. m=7
%o psumprm(m,n) = { sr=0; s=0; for(j=1,m, s+=prime(j); ); for(x=1,n, s = s - prime(x)+ prime(x+m); if(isprime(s),sr+=1.0/s; print1(s" ")); ); print(); print(sr) }
%Y Cf. A180948.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, May 09 2003
%E Corrected by _Michael Somos_, Feb 01 2004
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