A077220 a(1) = 1; thereafter a(n) is smallest number not occurring earlier such that a(n-1)+a(n) is a triangular number.
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
Offset: 1
Examples
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.
Links
Programs
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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 *) -
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
Extensions
More terms from Reinhard Zumkeller, Sep 28 2004
Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007
Further edited by N. J. A. Sloane, Jul 11 2010, Jul 19 2010
Comments