A128923 a(1) = a(2) = 1. a(n) = number of terms among (a(1),a(2),...a(n-1)) that divide (a(n-1) + a(n-2)).

1, 1, 2, 2, 4, 4, 6, 4, 4, 8, 9, 2, 2, 10, 11, 2, 2, 12, 8, 13, 2, 2, 14, 16, 12, 15, 3, 13, 17, 14, 2, 18, 16, 12, 17, 2, 2, 17, 2, 2, 19, 3, 16, 3, 3, 20, 2, 17, 3, 22, 2, 32, 21, 2, 2, 23, 2, 2, 25, 8, 8, 32, 31, 9, 31, 31, 24, 3, 10, 4, 23, 10, 9, 3, 37, 34, 2, 42, 29, 2, 5, 2, 2, 30, 39

Offset

1,3

Comments

From Robert G. Wilson v, Apr 29 2007: (Start)

a(n) = 2 for n's: 3, 4, 12, 13, 16, 17, 21, 22, 31, 36, 37, 39, 40, 47, 51, 54, 55, 57, 58, ..., .

First occurrence of k: 1, 3, 27, 5, 81, 7, 118, 10, 11, 14, 15, 18, 20, 23, 26, 24, 29, 32, 41, 46, ..., . (End)

Links

Table of n, a(n) for n=1..85.

Example

a(6) + a(7) = 10. 10 is divisible by a(1)=1, a(2)=1, a(3)=2, a(4)=2 and is not divisible by any other of the first 7 terms. So a(8) = 4.

Maple

a[1]:=1: a[2]:=1: for n from 3 to 110 do ct:=0: for j from 1 to n-1 do if type((a[n-1]+a[n-2])/a[j], integer)=true then ct:=ct+1 else ct:=ct: fi od: a[n]:=ct: od: seq(a[n], n=1..110); # Emeric Deutsch, Apr 26 2007

Mathematica

f[s_List] := Block[{}, Append[s, Count[ Mod[ s[[ -1]] + s[[ -2]], s], 0]]]; Nest[f, {1, 1}, 85] (* Robert G. Wilson v *)

Crossrefs

Sequence in context: A377225 A354755 A354858 * A153835 A338098 A171462

Adjacent sequences: A128920 A128921 A128922 * A128924 A128925 A128926

Keyword

nonn

Author

Leroy Quet, Apr 25 2007

Extensions

More terms from Emeric Deutsch and Robert G. Wilson v, Apr 26 2007

Status

approved