A174721 Integers z that cannot be largest number in the group of consecutive positive integers, sum of whom is average of twin prime pairs.

1, 2, 4, 10, 13, 20, 31, 33, 48, 55, 64, 66, 70, 82, 98, 103, 241, 280

Offset

1,2

Comments

Consider a group of consecutive positive Integers : a+b+...+y+z = Average of twin prime pairs. Number 4:: 1+2+3+4=10, 2+3+4=9, 3+4=7. Total 3 possible combination; all 3 sums are Not averages of twin prime pairs; number 4 part of this sequence 1+2+3=6, 3+4+5=12 == averages of twin prime pairs, numbers 3 and 5 are Not in this sequence.

Links

Table of n, a(n) for n=1..18.

Mathematica

mx=2500; mz=mx+(mx+1); lst={}; Do[p=a; Do[p+=n; If[PrimeQ[p-1]&&PrimeQ[p+1], AppendTo[lst, n]], {n, a+1, mx+1}], {a, 1, mx}]; z=Union@lst; Complement[Range[mx], z]

Crossrefs

Cf. A014574, A174716, A174717

Sequence in context: A180427 A127591 A100912 * A026224 A034233 A056718

Adjacent sequences: A174718 A174719 A174720 * A174722 A174723 A174724

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Mar 28 2010

Status

approved