A080353 -id:A080353 - cp's OEIS frontend

A080354 First differences of A080353.

2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1

Offset: 0

N. J. A. Sloane, Mar 20 2003

nonn

Most[Table[#,3]&/@Table[PadRight[{2},n,1],{n,10}]//Flatten] (* Harvey P. Dale, Dec 08 2019 *)

Runs are 2^2, (2 1)^3, (2 1 1)^3, (2 1 1 1)^3, ...

A081840 a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

Original entry on oeis.org

0, 4, 8, 11, 15, 19, 23, 26, 30, 34, 37, 41, 45, 49, 52, 56, 60, 64, 67, 71, 75, 79, 82, 86, 90, 93, 97, 101, 105, 108, 112, 116, 120, 123, 127, 131, 134, 138, 142, 146, 149, 153, 157, 161, 164, 168, 172, 176, 179, 183, 187, 190, 194, 198, 202, 205, 209, 213, 217

Offset: 1

Benoit Cloitre, Apr 11 2003

nonn

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,3,4)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Benoit Cloitre, A study of a family of self-referential sequences, arXiv:2506.18103 [math.GM], 2025. See p. 9.
Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 3.

Cf. A080353, A080580, A080590, A080600, A080652, A080754, A081834.

Block[{c, k}, c[] := False; k = 0; c[0] = True; {k}~Join~Reap[Do[If[c[n], k += 3, k += 4]; c[k] = True; Sow[k], {n, 2, 120}]][[-1, 1]] ] (* _Michael De Vlieger, Jul 02 2025 *)

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

A081841 a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.

Original entry on oeis.org

0, 2, 4, 7, 9, 11, 14, 16, 19, 21, 24, 26, 28, 31, 33, 36, 38, 40, 43, 45, 48, 50, 52, 55, 57, 60, 62, 65, 67, 69, 72, 74, 77, 79, 81, 84, 86, 89, 91, 94, 96, 98, 101, 103, 106, 108, 110, 113, 115, 118, 120, 123, 125, 127, 130, 132, 135, 137, 139, 142, 144, 147, 149, 151

Offset: 1

Benoit Cloitre, Apr 11 2003

nonn

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,3,2)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Benoit Cloitre, A study of a family of self-referential sequences, arXiv:2506.18103 [math.GM], 2025. See p. 7.
Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See pp. 3, 8.

Cf. A080353, A080580, A080590, A080600, A080652, A080754, A081834, A081840

Block[{c, k}, c[] := False; k = 0; c[0] = True; {k}~Join~Reap[Do[If[c[n], k += 3, k += 2]; c[k] = True; Sow[k], {n, 2, 120}]][[-1, 1]] ] (* _Michael De Vlieger, Jul 02 2025 *)

a(1)=0; for n>=1 a(n)=floor(r*n-(4*r-1)/(r+1)) where r=1+sqrt(2)

A081842 a(1)=0, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.

Original entry on oeis.org

0, 3, 7, 10, 13, 16, 20, 23, 26, 30, 33, 36, 40, 43, 46, 50, 53, 56, 59, 63, 66, 69, 73, 76, 79, 83, 86, 89, 92, 96, 99, 102, 106, 109, 112, 116, 119, 122, 125, 129, 132, 135, 139, 142, 145, 149, 152, 155, 158, 162, 165, 168, 172, 175, 178, 182, 185, 188, 192, 195

Offset: 1

Benoit Cloitre, Apr 11 2003

nonn

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,0,4,3)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Michael De Vlieger, Table of n, a(n) for n = 1..10000
Benoit Cloitre, A study of a family of self-referential sequences, arXiv:2506.18103 [math.GM], 2025. See p. 7.
Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See p. 3.

Cf. A080353, A080580, A080590, A080600, A080652, A080754, A081834, A081840, A081841.

Module[{seq={0},n=2},Do[If[MemberQ[seq,n],AppendTo[seq,Last[seq]+4],AppendTo[seq, Last[seq]+3]];n++,{60}];seq] (* Harvey P. Dale, Nov 20 2012 *)

a(n) = floor(r*n-(4*r-1)/(r+1)) where r = (1/2)*(3+sqrt(13)).

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A080354 First differences of A080353.

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A081840 a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+4 otherwise.

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A081841 a(1)=0, a(n)=a(n-1)+3 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.

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A081842 a(1)=0, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+3 otherwise.

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