

A077220


a(1) = 1; thereafter a(n) is smallest number not occurring earlier such that a(n1)+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
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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 106=4 is in ss, hence a(5)=156=9;
n=6, ss={1,2,4,6,9}; triangular numbers > 9 are 10,15,21; but 109=4 and 159=6 are in ss, hence a(6)=219=12 etc.


MATHEMATICA

tr=Table[n(n+1)/2, {n, 100}]; s={1}; a=1; Do[Do[tk=tr[[k]]; If[tk > a, b=tka; 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



