A141579 Numbers k such that the arithmetic mean of the first k tribonacci numbers A000073 is an integer.
1, 2, 47, 53, 94, 103, 106, 163, 199, 206, 257, 269, 311, 326, 397, 398, 401, 419, 421, 499, 514, 538, 587, 599, 617, 622, 683, 757, 773, 794, 802, 838, 842, 863, 883, 907, 911, 929, 991, 998, 1021, 1087, 1109, 1123, 1174, 1181, 1198, 1210, 1234, 1237, 1291
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1500 from Harvey P. Dale)
Programs
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Maple
A000073 := proc(n) option remember ; if n <= 1 then 0 ; elif n =2 then 1 ; else procname(n-1)+procname(n-2)+procname(n-3) ; fi; end: A008937 := proc(n) option remember ; add(A000073(i),i=0..n+1) ; end: isA := proc(n) if n = 1 then RETURN(true) ; fi; if A008937(n-2) mod n = 0 then true; else false ; fi; end: for n from 1 to 2000 do if isA(n) then printf("%d,",n) ; fi; od ;
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Mathematica
Module[{nn=1300,tnos},tnos=LinearRecurrence[{1,1,1},{0,0,1},nn];Position[ Table[Mean[Take[tnos,n]],{n,nn}],?(IntegerQ[#]&)]]//Flatten (* _Harvey P. Dale, Oct 05 2020 *)
Formula
{k: k | A008937(k-2)}.
Comments