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a(1) = 1, a(2) = 1 and a(n) = number of terms among (a(1),a(2),...a(n-1)) which divide (a(n-1)+a(n-2)).
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%I #12 Sep 20 2024 05:44:51

%S 1,2,1,2,2,5,2,2,7,2,2,9,2,2,11,2,2,13,3,13,13,16,2,16,16,17,4,4,16,

%T 17,4,4,18,15,4,2,16,18,17,4,4,22,18,23,2,3,3,19,18,2,25,6,2,25,6,2,

%U 26,27,2,2,28,28,31,2,6,29,4,6,23,3,26,3,3,32,4,46,25,2,10,42,37,2,11,5,38,2

%N a(1) = 1, a(2) = 1 and a(n) = number of terms among (a(1),a(2),...a(n-1)) which divide (a(n-1)+a(n-2)).

%C a(n) = 2 for n's: 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 23, 36, 45, 50, 53, 56, 59, 60, 64, 78, 82, 86, ....

%C First occurrence of k: 1, 2, 19, 27, 6, 52, 9, 186, 12, 79, 15, 255, 18, 107, 34, 22, 26, 33, 48, 134, 205, 42, 44, 381, 51, ....

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

%Y Cf. A128923.

%K nonn

%O 1,2

%A _Robert G. Wilson v_ and _Leroy Quet_, Apr 29 2007