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A014132
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Complement of triangular numbers A000217.
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8
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2, 4, 5, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Numbers that are not triangular.
Also definable as follows: a(1)=2; for n>1, a(n) is smallest integer greater than a(n-1) such that the condition "n and a(a(n)) have opposite parities" can always be satisfied. - Benoit Cloitre and Matthew Vandermast, Mar 10 2003
Comment from Alford Arnold (Alford1940(AT)aol.com), Oct 20 2006: May also be viewed as a triangular table beginning
2
4 5
7 8 9
11 12 13 14
16 17 18 19 20
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LINKS
| B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
B. Cloitre, N. J. A. Sloane and M. J. Vandermast, Numerical analogues of Aronson's sequence (math.NT/0305308)
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FORMULA
| a(n) = n + round(sqrt(2*n)).
a(a(n)) = n + 2*[1/2 + sqrt(2n)] + 1, where [] is the integer part.
a(n) = a(n-1) + A035214(n), a(1)=2.
a(n) = A080036(n) - 1.
a(n) = n + A002024(n). - Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jul 08 2010
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MATHEMATICA
| f[n_] := n + Round[Sqrt[2n]]; Array[f, 71] (* or *)
Complement[ Range[83], Array[ #(# + 1)/2 &, 13]] (from Robert G. Wilson v (rgwv(at)rgwv.com), Oct 21 2005)
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PROG
| (PARI) a(n)=if(n<1, 0, n+(sqrtint(8*n-7)+1)\2)
(MAGMA) IsTriangular:=func< n | exists{ k: k in [1..Isqrt(2*n)] | n eq (k*(k+1) div 2)} >; [ n: n in [1..90] | not IsTriangular(n) ]; - Klaus Brockhaus, Jan 04 2011
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CROSSREFS
| Cf. A000217, A006002, A035214, A080036, A002024.
Sequence in context: A095042 A010423 A035235 * A184008 A183862 A047381
Adjacent sequences: A014129 A014130 A014131 * A014133 A014134 A014135
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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