A080905 -id:A080905 - cp's OEIS frontend

A080927 Where records occur in A080905 (endpoints of record runs).

Original entry on oeis.org

5, 198, 1281, 6162, 12749, 102883

Offset: 1

N. J. A. Sloane, Apr 04 2003

nonn

Cf. A080905, A080922, A080900.

A080922 Records in A080905.

Original entry on oeis.org

4, 7, 10, 21, 63, 81

Offset: 1

N. J. A. Sloane, Apr 04 2003

nonn

Cf. A080905, A080927, A080900.

A080900 a(1)=1; 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

1, 6, 11, 16, 21, 19, 24, 29, 34, 39, 37, 42, 47, 52, 57, 55, 60, 65, 63, 68, 66, 71, 76, 74, 79, 84, 89, 94, 92, 97, 102, 107, 112, 110, 115, 120, 118, 123, 121, 126, 131, 129, 134, 139, 144, 149, 147, 152, 157, 162, 167, 165, 170, 175, 173, 178, 176

Offset: 1

N. J. A. Sloane and Benoit Cloitre, Apr 01 2003

nonn

Antti Karttunen, Table of n, a(n) for n = 1..20000 (terms 1..1000 from Ivan Neretin)
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 p. 2.

Cf. A080912, A080913, A080904, A080914, A080578, A080919, A080922, A080927.

Cf. A080901 (starting value = 2), A080905 (run lengths of first differences).

Fold[Append[#1, #1[[-1]] + If[MemberQ[#1, #2], -2, 5]] &, {1}, Range[2, 57]] (* Ivan Neretin, Mar 03 2016 *)

up_to = 1001;
A080900list(up_to_n) = { my(xs=Map(), v=vector(up_to_n)); mapput(xs,1,1); v[1] = 1; for(n=2,up_to_n, v[n] = v[n-1]+if(mapisdefined(xs,n), -2, +5); mapput(xs,v[n],n)); (v); };
v080900 = A080900list(up_to);
A080900(n) = v080900[n]; \\ Antti Karttunen, Jan 22 2020

Perhaps this is asymptotic to c_0*n*(1 + c_1/log n + ...), with c_0 near 2 ?

cp's OEIS Frontend

A080927 Where records occur in A080905 (endpoints of record runs).

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A080922 Records in A080905.

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A080900 a(1)=1; 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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