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A055514
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Composite numbers that are the sum of consecutive prime numbers and are divisible by the first and last of these primes.
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6
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OFFSET
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1,1
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COMMENTS
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Composite n such that n = p_1 + p_2 + ... + p_k where the p_i are consecutive primes and n is divisible by p_1 and p_k.
Problem proposed by Carlos Rivera, who found the first 4 terms.
In subsequence A055233 the first and last term of the sum must also be its smallest and largest prime factor. Therefore a(5) (cf. first EXAMPLE) is not in that sequence, since it has smaller factors 2^3*5. - M. F. Hasler, Nov 21 2021
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LINKS
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EXAMPLE
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503 + 509 + 521 + ... + 508213 = 10225245560, which is divisible by 503 and 508213. - Manuel Valdivia, Nov 17 2011
a(8) = 7228559051256366318 = 73 + ... + 18281691653;
a(9) = 1390718713078158117206 = 370794889 + ... + 267902967061. (End)
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MATHEMATICA
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Module[{nn=200}, Table[Total/@Select[Partition[Prime[Range[10000]], n, 1], scpQ], {n, 2, nn}]]//Flatten (* The program generates the first four terms of the sequence. *)
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PROG
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(PARI) S=vector(N=50000); s=0; i=1; forprime(p=2, oo, S[i++]=s+=p; for(j=1, i-2, (s-S[j])%p || (s-S[j])%prime(j)|| print1(s-S[j]", ")|| break)) \\ gives a(1..5), but too slow to go beyond. - M. F. Hasler, Nov 21 2021
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CROSSREFS
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KEYWORD
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nice,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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