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A066706 Numbers k that divide the average of prime(k) and prime(k+1). 2
2, 3, 10, 30, 182, 439, 1058, 40086, 40090, 40114, 40120, 100347, 251708, 637328, 637336, 637340, 4124468, 10553440, 10553445, 10553829, 27067138, 179992932, 179993008, 179993012, 179993017, 465769835 (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. - Robert G. Wilson v, Jan 18 2002

LINKS

Table of n, a(n) for n=1..26.

EXAMPLE

The average of p(3) = 5 and p(3+1) = 7 is 6, which is divisible by 3; so 3 is a term of the sequence.

MATHEMATICA

Select[ Range[10^7], Mod[ (Prime[ # + 1] + Prime[ # ])/2, # ] == 0 & ]

a = 2; b = 3; Do[b = Prime[n + 1]; If[ Mod[(a + b)/2, n] == 0, Print[n]]; a = b, {n, 1, 2*10^9} ]

CROSSREFS

Sequence in context: A338593 A270363 A131764 * A209003 A080022 A192913

Adjacent sequences:  A066703 A066704 A066705 * A066707 A066708 A066709

KEYWORD

nonn

AUTHOR

Joseph L. Pe, Jan 14 2002

EXTENSIONS

More terms from Robert G. Wilson v, Jan 16 2002

More terms from Robert G. Wilson v, Jan 18 2002

STATUS

approved

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Last modified September 21 21:32 EDT 2021. Contains 347605 sequences. (Running on oeis4.)