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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

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OFFSET

1,1

LINKS

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

EXAMPLE

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)

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 *)

PROG

(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) }

CROSSREFS

Cf. A180948.

Sequence in context: A171383 A182572 A152625 * A159809 A345551 A051371

Adjacent sequences: A082243 A082244 A082245 * A082247 A082248 A082249

KEYWORD

easy,nonn

AUTHOR

Cino Hilliard, May 09 2003

EXTENSIONS

Corrected by Michael Somos, Feb 01 2004

STATUS

approved