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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

Index entries for sequences that are permutations of the natural numbers

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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Last modified March 25 01:30 EDT 2017. Contains 284036 sequences.