A081843 - OEIS

%I #17 Aug 16 2021 17:51:08

%S 0,4,8,13,17,21,25,30,34,38,42,46,51,55,59,63,68,72,76,80,85,89,93,97,

%T 102,106,110,114,118,123,127,131,135,140,144,148,152,157,161,165,169,

%U 174,178,182,186,191,195,199,203,207,212,216,220,224,229,233,237,241

%N a(1)=0, a(n)=a(n-1)+5 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

%C A high proportion of terms are the same as A004938, which is the nearest integer to n*r, where r=2+sqrt(5) as defined in the formula section. Allowing for the difference in offset, the first 3 terms to differ are those which have values 46, 63 and 118 instead of 47, 64 and 119. - _Peter Munn_, Aug 07 2019

%H Jinyuan Wang, <a href="/A081843/b081843.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = floor(r*n-(5*r-1)/(r+1)) where r=2+sqrt(5).

%t Clear[used];used={}; nxt[{n_,a_}]:=Module[{c=If[MemberQ[ used,n+1],5,4]},Flatten[ AppendTo[ used,a+c]];{n+1,c+a}]; NestList[nxt,{1,0},60][[All,2]] (* _Harvey P. Dale_, Aug 16 2021 *)

%Y Cf. A004938, A081835, A081839.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Apr 11 2003