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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
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
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 * A353052 A209003 A080022
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