cp's OEIS Frontend

A080633 a(1)=3; for n > 1, a(n) is the smallest integer greater than a(n-1) consistent with the condition "n is in the sequence if and only if a(n) is congruent to 1 (mod 4)".

%I A080633 #13 Aug 22 2025 06:28:00
%S A080633 3,4,5,9,13,14,15,16,17,18,19,20,21,25,29,33,37,41,45,49,53,54,55,56,
%T A080633 57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,
%U A080633 80,81,82,83,84,85,89,93,97,101,105,109,113,117,121,125,129,133,137,141
%N A080633 a(1)=3; for n > 1, a(n) is the smallest integer greater than a(n-1) consistent with the condition "n is in the sequence if and only if a(n) is congruent to 1 (mod 4)".
%C A080633 Equivalently: unique monotonic sequence satisfying a(1)=3, a(a(n))=4n+1.
%H A080633 B. 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 A080633 B. Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a> (math.NT/0305308)
%H A080633 <a href="/index/Aa#aan">Index entries for sequences of the a(a(n)) = 2n family</a>
%F A080633 There is an explicit formula for a(n) similar to that for A079000.
%K A080633 nonn
%O A080633 1,1
%A A080633 _Benoit Cloitre_, Feb 23 2003
%E A080633 More terms from _Matthew Vandermast_, Mar 13 2003