A086447 -id:A086447 - cp's OEIS frontend

A086448 a(n) = the least integer of the form [prime(n+1)+prime(n+2)+...+prime(n+k)]/prime(n).

4, 4, 18, 16, 12, 12, 6, 16, 6, 102, 11, 93, 119, 345, 48, 240, 138, 100, 263, 19, 227, 282, 31, 1071, 11, 126, 386, 278, 184, 642, 164, 445, 55, 213, 89, 190, 895, 1120, 61, 258, 4629, 323, 122, 789, 5226, 59, 1292, 325, 364, 374, 430, 3939, 118, 695, 87, 73, 358

Offset: 1

Zak Seidov, Jul 20 2003

It seems that a(n) exists for any n.
Among first 1000 terms, the largest term is a(793) = 1807606, with p = prime(793) = 6079, and 6079*1807606 = the sum of 42840 consecutive primes after p. - Zak Seidov, Nov 07 2014
Among first 10000 terms, the largest term is a(9349) = 30376745, with p = prime(9349) = 97159, and p*(9349) = the sum of 629543 consecutive primes after p: 2951374167455 = sum(prime(k), k = 9349 + 1..9349 + 629543) - Zak Seidov, Feb 21 2015

			a(3)=18 because prime(3)=5 and (7+11+13+17+19+23)/5 = 18.

Zak Seidov, Table of n, a(n) for n = 1..10000

Cf. A055233, A055514, A086447.

bb={}; Do[s0=Prime[n0]; s=0; Do[If[IntegerQ[ss0=(s+=Prime[n])/s0], bb=Append[bb, ss0]; Break[]], {n, n0+1, 8000}], {n0, 1, 10}]; bb

Edited by Don Reble, Nov 10 2005

A200721 Product of two nonconsecutive primes p and q that divides the sum of primes between p and q, exclusively.

Original entry on oeis.org

26, 1133, 20309, 51159, 3246905, 28673661, 5201685791

Offset: 1

Manuel Valdivia, Nov 21 2011

nonn

Prime p is approximately q/((2*log(q)-1)*k), for k = 1, 1, 3, 307, 5041, 102378,..(quotients).

a(8) > 2*10^10. 3235398421447 is also a term. - Donovan Johnson, Nov 23 2011

			51159 = 3*17053, (5+ ... +17047)/51159 = 307.

Cf. A055514, A055233, A086447, A086448, A001358.

ss[n_] := Module[{f = Transpose[FactorInteger[n]], p, q, s}, If[f[[2]] == {1, 1}, {p, q} = PrimePi[f[[1]]]; s = Total[Table[Prime[i], {i, p + 1, q - 1}]]; s != 0 && Mod[s, n] == 0, False]]; Select[Range[2, 21000], ss] (* T. D. Noe, Nov 21 2011 *)

a(7) from Donovan Johnson, Nov 23 2011

cp's OEIS Frontend

A086448 a(n) = the least integer of the form [prime(n+1)+prime(n+2)+...+prime(n+k)]/prime(n).

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