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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. 3
 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, 42, 49, 56, 22, 14, 41, 37, 18, 27, 28, 38, 40, 51, 54, 66, 39, 52, 53, 67, 69, 84, 87, 33, 45, 46, 32, 23, 43, 35, 70, 50, 55, 65, 71, 34, 44, 47, 58, 62, 74, 79, 57, 48, 72, 64, 89 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS Zak Seidov, Table of n, a(n) for n = 1..1000 EXAMPLE 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; 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. MATHEMATICA 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 *) PROG (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 CROSSREFS Cf. A000217, A125595, A125630, A099130. Sequence in context: A247185 A237685 A220768 * A128716 A258934 A225600 Adjacent sequences:  A077217 A077218 A077219 * A077221 A077222 A077223 KEYWORD nonn,easy AUTHOR Amarnath Murthy, Nov 03 2002 EXTENSIONS More terms from Reinhard Zumkeller, Sep 28 2004 Edited by N. J. A. Sloane at the suggestion of Andrew Plewe, Jun 08 2007 Further edited by N. J. A. Sloane, Jul 11 2010, Jul 19 2010 STATUS approved

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