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A077220 a(1) = 1; thereafter a(n) is smallest number not occurring earlier such that a(n-1)+a(n) is a triangular number.

%I A077220 #25 Sep 24 2018 16:53:14
%S A077220 1,2,4,6,9,12,3,7,8,13,15,21,24,31,5,10,11,17,19,26,29,16,20,25,30,36,
%T A077220 42,49,56,22,14,41,37,18,27,28,38,40,51,54,66,39,52,53,67,69,84,87,33,
%U A077220 45,46,32,23,43,35,70,50,55,65,71,34,44,47,58,62,74,79,57,48,72,64,89
%N A077220 a(1) = 1; thereafter a(n) is smallest number not occurring earlier such that a(n-1)+a(n) is a triangular number.
%C A077220 Conjectured to be a permutation of the natural numbers (cf. A099130). The first few fixed points are: 1, 2, 19, 92, 220, 467, 556, 616, 690, 842.
%H A077220 Zak Seidov, <a href="/A077220/b077220.txt">Table of n, a(n) for n = 1..1000</a>
%H A077220 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A077220 n=5: ss={1,2,4,6}; triangular numbers > 6 are 10,15,21; but 10-6=4 is in ss, hence a(5)=15-6=9;
%e A077220 n=6, ss={1,2,4,6,9}; triangular numbers > 9 are 10,15,21; but 10-9=4 and 15-9=6 are in ss, hence a(6)=21-9=12 etc.
%t A077220 tr=Table[n(n+1)/2, {n, 100}]; s={1}; a=1; Do[Do[tk=tr[[k]]; If[tk > a, b=tk-a; If[FreeQ[s, b], AppendTo[s, b]; a=b; Break[]]], {k, 100}], {99}]; s (* _Zak Seidov_, Jul 12 2010 *)
%o A077220 (PARI) v=[1]; n=1; while(n<100, if(ispolygonal(n+v[#v],3)&&!vecsearch(vecsort(v), n), v=concat(v, n); n=0); n++); v \\ _Derek Orr_, Jun 08 2015
%Y A077220 Cf. A000217, A125595, A125630, A099130.
%K A077220 nonn,easy
%O A077220 1,2
%A A077220 _Amarnath Murthy_, Nov 03 2002
%E A077220 More terms from _Reinhard Zumkeller_, Sep 28 2004
%E A077220 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 08 2007
%E A077220 Further edited by _N. J. A. Sloane_, Jul 11 2010, Jul 19 2010