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A082246 Primes that are the sum of 7 consecutive primes. 16
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
easy,nonn
AUTHOR
Cino Hilliard, May 09 2003
EXTENSIONS
Corrected by Michael Somos, Feb 01 2004
STATUS
approved

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Last modified March 1 20:05 EST 2024. Contains 370443 sequences. (Running on oeis4.)