A081835 -id:A081835 - cp's OEIS frontend

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

Benoit Cloitre, Apr 11 2003

nonn

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

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,5,4)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Jinyuan Wang, Table of n, a(n) for n = 1..1000
Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 3.

Cf. A004938, A081835, A081839.

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 *)

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

A081839 a(1)=0, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

Original entry on oeis.org

0, 5, 10, 15, 19, 24, 29, 34, 39, 43, 48, 53, 58, 63, 67, 72, 77, 82, 86, 91, 96, 101, 106, 110, 115, 120, 125, 130, 134, 139, 144, 149, 154, 158, 163, 168, 173, 178, 182, 187, 192, 197, 201, 206, 211, 216, 221, 225, 230, 235, 240, 245, 249, 254, 259, 264, 269

Offset: 1

Benoit Cloitre, Apr 11 2003

nonn

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,4,5)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 3.

Cf. A081834, A081835, A081840, A081841, A081842, A081843.

cloitreH[j_, x_, y_, z_, w_ : 120] := Module[{c, k}, c[] := False; k = x; c[x] = True; {x}~Join~Reap[Do[If[c[n - j], k += y, k += z]; c[k] = True; Sow[k], {n, 2, w}] ][[-1, 1]] ]; cloitreH[0, 0, 4, 5] (* _Michael De Vlieger, Jul 29 2025 *)

a(n) = floor(r*n-(3*r+1)/(r-1)) where r = (1/2) *(5+sqrt(21)) = 4.79128784747792...

cp's OEIS Frontend

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

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