A081843 a(1)=0, a(n)=a(n-1)+5 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

0, 4, 8, 13, 17, 21, 25, 30, 34, 38, 42, 46, 51, 55, 59, 63, 68, 72, 76, 80, 85, 89, 93, 97, 102, 106, 110, 114, 118, 123, 127, 131, 135, 140, 144, 148, 152, 157, 161, 165, 169, 174, 178, 182, 186, 191, 195, 199, 203, 207, 212, 216, 220, 224, 229, 233, 237, 241

Offset

1,2

Comments

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

Links

Jinyuan Wang, Table of n, a(n) for n = 1..1000

Formula

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

Mathematica

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 *)

Crossrefs

Cf. A004938, A081835, A081839.

Sequence in context: A311814 A311815 A311816 * A004938 A299641 A311817

Adjacent sequences: A081840 A081841 A081842 * A081844 A081845 A081846

Keyword

nonn

Author

Benoit Cloitre, Apr 11 2003

Status

approved