A082246 Primes that are the sum of 7 consecutive primes.

197, 223, 251, 281, 311, 401, 431, 463, 523, 593, 659, 719, 757, 827, 863, 947, 991, 1063, 1171, 1753, 1901, 2347, 2393, 2647, 2689, 2731, 2777, 2819, 2953, 3347, 3389, 3533, 3643, 3701, 3761, 3821, 4177, 4217, 4451, 4493, 5507, 5717, 5849, 5927, 6029

Offset: 1

Author

Cino Hilliard, May 09 2003

Keywords

• easy
• nonn

Examples

			2 + 3 + 5 + 7 + 11 + 13 + 17 = 58 = 2*29
3 + 5 + 7 + 11 + 13 + 17 + 19 = 75 = 3*5^2
5 + 7 + 11 + 13 + 17 + 19 + 23 = 95 = 5*19
7 + 11 + 13 + 17 + 19 + 23 + 29 = 119 = 7*17
11 + 13 + 17 + 19 + 23 + 29 + 31 = 143 = 11*13
13 + 17 + 19 + 23 + 29 + 31 + 37 = 169 = 13*13
17 + 19 + 23 + 29 + 31 + 37 + 41 = 197 (prime)
		

Links

• Syed Iddi Hasan, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A180948.

Programs

Maple

Primes:= select(isprime, [seq(i,i=3..10000,2)]):
S:= ListTools:-PartialSums(Primes):
select(isprime,S[8..-1]-S[1..-8]); # Robert Israel, Dec 14 2017

Mathematica

Select[ListConvolve[{1,1,1,1,1,1,1},Prime[Range[200]]],PrimeQ] (* Harvey P. Dale, Jul 12 2013 *)
Select[Total/@Partition[Prime[Range[200]],7,1],PrimeQ] (* Harvey P. Dale, Jul 24 2017 *)

PARI

\\ primes in the sum of m odd number of consecutive primes. m=7
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) }

Extensions

Corrected by Michael Somos, Feb 01 2004