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A086447 a(n) = the least k such that prime(n+1)+prime(n+2)+...+prime(n+k) is a multiple of prime(n). 3
2, 2, 6, 6, 6, 6, 4, 8, 4, 30, 7, 31, 37, 67, 22, 60, 46, 38, 69, 13, 65, 76, 19, 163, 9, 52, 100, 84, 66, 136, 66, 119, 33, 79, 47, 76, 187, 214, 37, 96, 461, 111, 62, 189, 510, 37, 256, 121, 130, 132, 144, 481, 64, 195, 53, 47, 136, 90, 194, 318, 526, 151, 788, 1542 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: a(n) exists for every n.

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

EXAMPLE

a(3)=6 because prime(3)=5 divides 7+11+13+17+19+23 = 90.

MATHEMATICA

bb={}; Do[s0=Prime[n0]; s=0; Do[s+=Prime[n]; If[IntegerQ[s/s0], bb=Append[bb, n-n0]; Break[]], {n, n0+1, 8000}], {n0, 1, 100}]; bb

sncp[n_]:=Module[{p=Prime[n], k=n+1, t}, t=Prime[k]; While[!Divisible[ t, p], k++; t=t+Prime[k]]; k-n]; Array[sncp, 100]  (* Harvey P. Dale, May 21 2017 *)

PROG

(PARI) a(n)=my(p = prime(n), sp = nextprime(p+1), lp = sp, nb = 1); while (sp % p, lp = nextprime(lp+1); nb++; sp += lp); nb; \\ Michel Marcus, May 21 2017

(PARI) a(n, p=prime(n))=my(s, k); forprime(q=p+1, , s+=q; k++; if(s%p==0, return(k))) \\ Charles R Greathouse IV, May 21 2017

CROSSREFS

Cf. A055233, A055514, A086448.

Sequence in context: A185421 A219976 A063944 * A324032 A196872 A319865

Adjacent sequences:  A086444 A086445 A086446 * A086448 A086449 A086450

KEYWORD

easy,nonn

AUTHOR

Zak Seidov, Jul 20 2003

EXTENSIONS

Edited by Don Reble, Nov 10 2005

STATUS

approved

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Last modified October 20 12:40 EDT 2019. Contains 328257 sequences. (Running on oeis4.)