A066828 Numbers k that divide the average of prime(k-1) and prime(k+1).

4, 5, 11, 12, 70, 72, 1053, 6459, 6460, 40083, 251742, 637320, 637322, 637330, 10553828, 69709721, 179992913, 179992922, 465769813, 1208198617, 1208198629, 3140421742, 3140421769, 3140421866, 8179002192, 8179002205, 8179002209

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..27.

Example

The average of prime(4) = 7 and prime(6) = 13 is 10, which is divisible by 5, so 5 is a term of the sequence.

Mathematica

a = 0; b = 1; c = 2; Do[ c = Prime[ n + 1 ]; If[ IntegerQ[ (a + c)/(2n) ], Print[ n ] ]; a = b; b = c, {n, 1, 2 10^9} ]
Select[Range[2, 41000], Mod[(Prime[#-1]+Prime[#+1])/2, #]==0&] (* The program generates the first 10 terms of the sequence. *) (* Harvey P. Dale, Feb 21 2026 *)

Crossrefs

Cf. A066706.

Sequence in context: A047374 A241653 A100107 * A163098 A216562 A174009

Adjacent sequences: A066825 A066826 A066827 * A066829 A066830 A066831

Keyword

nonn

Author

Robert G. Wilson v, Jan 20 2002

Status

approved