OFFSET
1,1
COMMENTS
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.
No more terms below 10^22. - Michael Beight, Jul 22 2012
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
LINKS
C. Rivera, Puzzle
EXAMPLE
503 + 509 + 521 + ... + 508213 = 10225245560, which is divisible by 503 and 508213. - Manuel Valdivia, Nov 17 2011
From Michael Beight, Jul 22 2012: (Start)
a(8) = 7228559051256366318 = 73 + ... + 18281691653;
a(9) = 1390718713078158117206 = 370794889 + ... + 267902967061. (End)
MATHEMATICA
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. *)
(* Harvey P. Dale, Oct 22 2022 *)
PROG
(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
CROSSREFS
KEYWORD
nice,nonn
AUTHOR
Jud McCranie, Jul 03 2000
EXTENSIONS
a(7) from Donovan Johnson, Jun 19 2008
a(8) and a(9) from Michael Beight, Jul 22 2012
STATUS
approved