A084736 a(1) = 2, a(2) = 3; for n > 0, a(n+2) is the smallest prime chosen so that (a(n+2) - a(n+1))/(a(n+1) - a(n)) is an integer.

2, 3, 5, 7, 11, 19, 43, 67, 139, 211, 283, 499, 1579, 2659, 3739, 8059, 12379, 16699, 21019, 25339, 38299, 103099, 167899, 232699, 491899, 1787899, 9563899, 17339899, 25115899, 40667899, 71771899, 196187899, 818267899, 4550747899, 15748187899

Offset

1,1

Comments

Successive differences are multiples of the previous difference.

Links

Table of n, a(n) for n=1..35.

Example

43, 67 and 139 are three successive terms and (139-67)/(67-43) = 3.

Mathematica

a[0] = 2; a[1] = 3; a[n_] := a[n] = Block[{k = 1}, While[ !PrimeQ[ k( a[n - 1] - a[n - 2]) + a[n - 1]], k++ ]; k(a[n - 1] - a[n - 2]) + a[n - 1]]; Table[ a[n], {n, 0, 34}]

Crossrefs

Sequence in context: A002231 A087769 A308510 * A089472 A373045 A079429

Adjacent sequences: A084733 A084734 A084735 * A084737 A084738 A084739

Keyword

nonn

Author

Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 14 2003

Extensions

Edited and extended by Robert G. Wilson v and Vladeta Jovovic, Jun 17 2003

Status

approved