A066826 Numbers k that divide the average of prime(k-1) and prime(k).

6, 13, 14, 15, 74, 190, 6456, 40082, 251735, 251736, 251738, 637325, 637326, 637342, 637343, 4124456, 4124458, 10553425, 10553433, 10553818, 27067038, 27067053, 69709872, 69709877, 69709945, 69709954, 179992917, 179992920, 179993011, 179993025, 179993170

Offset

1,1

Comments

Each cluster of candidates is about e (2.71828...) times as large as the previous one.

Links

Table of n, a(n) for n=1..31.

Example

The average of prime(6-1) = 11 and prime(6) = 13 is 12, which is divisible by 6, so 6 is a term of the sequence.

Mathematica

a = 1; b = 2; Do[ b = Prime[ n ]; If[ IntegerQ[ (a + b)/(2n) ], Print[ n ] ]; a = b, {n, 1, 2*10^8} ]
With[{nn=30000000}, Last[#]&/@Select[Thread[{Partition[Prime[Range[nn]], 2, 1], Range[2, nn]}], Divisible[ Mean[First[#]], Last[#]]&]] (* Harvey P. Dale, Oct 21 2011 *) (* The program takes a long time to generate the first 22 terms of the sequence; to generate them all, by increasing nn, may overwhelm computer resources and operator patience *)

Crossrefs

Cf. A066706.

Sequence in context: A106623 A115010 A244535 * A031113 A112610 A100205

Adjacent sequences: A066823 A066824 A066825 * A066827 A066828 A066829

Keyword

nonn

Author

Robert G. Wilson v, Jan 20 2002

Extensions

a(29)-a(31) from D. S. McNeil, Oct 22 2011

Status

approved