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A077220
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a(1) = 1; thereafter a(n) is smallest number not occurring earlier such that a(n-1)+a(n) is a triangular number.
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2
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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; internal format)
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OFFSET
| 1,2
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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.
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LINKS
| Zak Seidov, Table of n, a(n) for n = 1..1000
Index entries for sequences that are permutations of the natural numbers
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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.
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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 (zakseidov(AT)yahoo.com), Jul 12 2010
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CROSSREFS
| Cf. A000217, A125595, A125630, A099130.
Sequence in context: A038107 A195526 A153196 * A128716 A183422 A025057
Adjacent sequences: A077217 A077218 A077219 * A077221 A077222 A077223
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KEYWORD
| nonn
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AUTHOR
| Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 03 2002
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EXTENSIONS
| More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 28 2004
Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 08 2007
Further edited by N. J. A. Sloane, Jul 11 2010, Jul 19 2010
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