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A082246
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Primes that are the sum of 7 consecutive primes.
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16
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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
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1,1
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LINKS
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EXAMPLE
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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)
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MAPLE
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Primes:= select(isprime, [seq(i, i=3..10000, 2)]):
S:= ListTools:-PartialSums(Primes):
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MATHEMATICA
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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 *)
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PROG
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(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) }
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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