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A066826 Numbers k that divide the average of prime(k-1) and prime(k). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 11:12 EDT 2021. Contains 347606 sequences. (Running on oeis4.)