cp's OEIS Frontend

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.

%I A080900 #25 Jul 29 2025 15:57:18
%S A080900 1,6,11,16,21,19,24,29,34,39,37,42,47,52,57,55,60,65,63,68,66,71,76,
%T A080900 74,79,84,89,94,92,97,102,107,112,110,115,120,118,123,121,126,131,129,
%U A080900 134,139,144,149,147,152,157,162,167,165,170,175,173,178,176
%N 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.
%H A080900 Antti Karttunen, <a href="/A080900/b080900.txt">Table of n, a(n) for n = 1..20000</a> (terms 1..1000 from Ivan Neretin)
%H A080900 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H A080900 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="https://arxiv.org/abs/math/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.
%H A080900 Robbert Fokkink and Gandhar Joshi, <a href="https://arxiv.org/abs/2507.16956">On Cloitre's hiccup sequences</a>, arXiv:2507.16956 [math.CO], 2025. See p. 2.
%F A080900 Perhaps this is asymptotic to c_0*n*(1 + c_1/log n + ...), with c_0 near 2 ?
%t A080900 Fold[Append[#1, #1[[-1]] + If[MemberQ[#1, #2], -2, 5]] &, {1}, Range[2, 57]] (* _Ivan Neretin_, Mar 03 2016 *)
%o A080900 (PARI)
%o A080900 up_to = 1001;
%o A080900 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); };
%o A080900 v080900 = A080900list(up_to);
%o A080900 A080900(n) = v080900[n]; \\ _Antti Karttunen_, Jan 22 2020
%Y A080900 Cf. A080912, A080913, A080904, A080914, A080578, A080919, A080922, A080927.
%Y A080900 Cf. A080901 (starting value = 2), A080905 (run lengths of first differences).
%K A080900 nonn
%O A080900 1,2
%A A080900 _N. J. A. Sloane_ and _Benoit Cloitre_, Apr 01 2003