A080578 -id:A080578 - cp's OEIS frontend

A080939 a(1)=3; for n>1, a(n)=a(n-1)-2 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

3, 8, 6, 11, 16, 14, 19, 17, 22, 27, 25, 30, 35, 33, 38, 36, 34, 39, 37, 42, 47, 45, 50, 55, 53, 58, 56, 61, 66, 64, 69, 74, 72, 70, 68, 66, 64, 62, 60, 65, 70, 68, 73, 78, 76, 81, 79, 84, 89, 87, 92, 97, 95, 100, 98, 96, 101, 99, 104, 102, 100, 98, 103, 101, 99

Offset: 1

N. J. A. Sloane and Benoit Cloitre, Apr 04 2003

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)

Cf. A080578, A080900, A080901.

a(n)-n (n >= 1) is periodic with period 168.

A080903 a(1)=1; for n>1, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.

Original entry on oeis.org

1, 3, 7, 9, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 39, 41, 45, 47, 51, 53, 55, 57, 61, 63, 67, 69, 71, 73, 77, 79, 83, 85, 87, 89, 93, 95, 99, 101, 105, 107, 111, 113, 115, 117, 121, 123, 127, 129, 131, 133, 137, 139, 143, 145, 149, 151, 155, 157, 159

Offset: 1

Benoit Cloitre, Apr 01 2003

nonn

In the Fokkink-Joshi paper, this sequence is the Cloitre (0,1,4,2)-hiccup sequence. - Michael De Vlieger, Jul 29 2025

Ivan Neretin, Table of n, a(n) for n = 1..1000
Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, arXiv:math/0305308 [math.NT], 2003.
Robbert Fokkink and Gandhar Joshi, On Cloitre's hiccup sequences, arXiv:2507.16956 [math.CO], 2025. See pp. 2-3.

Cf. A080578, A080900, A086398.

Fold[Append[#1, #1[[-1]] + If[MemberQ[#1, #2], 4, 2]] &, {1}, Range[2, 59]] (* Ivan Neretin, Mar 03 2016 *)

A080949 a(1)=0; for n>1, a(n)=a(n-1)-2 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

Original entry on oeis.org

0, 5, 10, 15, 13, 18, 23, 28, 33, 31, 36, 41, 39, 44, 42, 47, 52, 50, 55, 60, 65, 70, 68, 73, 78, 83, 88, 86, 91, 96, 94, 99, 97, 102, 107, 105, 110, 115, 113, 118, 116, 114, 119, 117, 122, 127, 125, 130, 135, 133, 138, 136, 141, 146, 144, 149, 154, 159

Offset: 1

N. J. A. Sloane and Benoit Cloitre, Apr 04 2003

nonn

B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)

Cf. A080578, A080900, A080901, A080939.

A126091 a(1)=1;a(2)=4; for n>2, a(n)=a(n-2)+3 if n is already in the sequence, a(n)=a(n-2)+1 otherwise.

Original entry on oeis.org

1, 4, 2, 7, 3, 8, 6, 11, 7, 12, 10, 15, 11, 16, 14, 19, 15, 20, 18, 23, 19, 24, 22, 27, 23, 28, 26, 31, 27, 32, 30, 35, 31, 36, 34, 39, 35, 40, 38, 43, 39, 44, 42, 47, 43, 48, 46, 51, 47, 52, 50, 55, 51, 56, 54, 59, 55, 60, 58, 63, 59, 64, 62, 67, 63, 68, 66, 71, 67, 72, 70, 75

Offset: 1

Zak Seidov, Mar 11 2007

nonn

Cf. A080578, A080455-A080458.

a={1,4};Do[If[MemberQ[a,n],b=a[[n-2]]+3,b=a[[n-2]]+1];AppendTo[a,b],{n,3,70}];a

cp's OEIS Frontend

A080939 a(1)=3; for n>1, a(n)=a(n-1)-2 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

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A080903 a(1)=1; for n>1, a(n)=a(n-1)+4 if n is already in the sequence, a(n)=a(n-1)+2 otherwise.

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A080949 a(1)=0; for n>1, a(n)=a(n-1)-2 if n is already in the sequence, a(n)=a(n-1)+5 otherwise.

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A126091 a(1)=1;a(2)=4; for n>2, a(n)=a(n-2)+3 if n is already in the sequence, a(n)=a(n-2)+1 otherwise.

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