A066706 Numbers k that divide the average of prime(k) and prime(k+1).

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

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 * A353052 A209003 A080022

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