%I A026272
%S A026272 1,2,1,3,2,4,5,3,6,7,4,8,5,9,10,6,11,7,12,13,8,14,15,9,16,10,
%T A026272 17,18,11,19,20,12,21,13,22,23,14,24,15,25,26,16,27,28,17,29,
%U A026272 18,30,31,19,32,20,33,34,21,35,36,22,37,23,38,39,24,40,41,25
%N A026272 a(n) = a(m) if a(m) has already occurred exactly once and n = a(m) + 
               m + 1, else a(n) = least positive integer that has not yet occurred.
%C A026272 This sequence displays every positive integer exactly twice and the gap 
               between the two occurrences of n contains exactly n other values. 
               The first occurrence of n precedes the first occurrence of n+1. (cont.)
%C A026272 Also related to the Wythoff array (A035513) and the Para-Fibonacci sequence 
               (A035513) where every positive integer is displayed exactly once 
               in the whole array. Take any integer n in A026272 and let C = number 
               of terms from the beginning of the sequence to the second occurrence 
               of n. Then C = (2nd term after n in the applicable sequence for n 
               in A035513). (cont.)
%C A026272 Also in the second occurrence of n in A026272, let N=n ( - one term) 
               = (first term value after n in the applicable sequence for n in A035513). 
               In this format the second occurrence of n in A026272 will produce 
               in A035513, n itself and two of the succeeding terms of n in the 
               Wythoff array where every positive integer can only be displayed 
               once. (cont.)
%C A026272 In A026272 if |a(n)-a(n+1)| > 10 then phi ~ a(n)/|a(n)-a(n+1)|. When 
               n -> infinity it will converge to phi. - Dan Joyce (danj_536(AT)msn.com), 
               Apr 13 2001
%C A026272 Or, put a copy of n in A000027 n places further along! - Zak Seidov (zakseidov(AT)yahoo.com), 
               May 24 2008
%C A026272 Another version would prefix this sequence with two leading 0's (see 
               the Angelini reference). If we use this form and write down the indices 
               of the two 0's, the two 1's, the two 2's, the two 3's, etc., then 
               we get A072061. - Jacques ALARDET (jacques.alardet(AT)free.fr), Jul 
               26 2008
%D A026272 E. Angelini, "Jeux de suites", in Dossier Pour La Science, pp. 32-35, 
               Volume 59 (Jeux math'), April/June 2008, Paris.
%H A026272 Zak Seidov, <a href="b026272.txt">Table of n, a(n) for n = 1..1000.</
               a>
%t A026272 s=Range[1000];n=0;Do[n++;s=Insert[s,n,Position[s,n][[1]]+n+1],{500}];
               A026272=Take[s,1000] - Zak Seidov (zakseidov(AT)yahoo.com), May 24 
               2008
%Y A026272 a(n) = A026242(n+2) - 1 = A026350(n+3) - 2 = A026354(n+4) - 3.
%Y A026272 Cf. A000027, A035513.
%Y A026272 Sequence in context: A034391 A144241 A094173 this_sequence A022447 A117194 
               A024467
%Y A026272 Adjacent sequences: A026269 A026270 A026271 this_sequence A026273 A026274 
               A026275
%K A026272 nonn,easy,nice
%O A026272 1,2
%A A026272 Clark Kimberling (ck6(AT)evansville.edu)