

A080036


a(n) = n + round(sqrt(2*n)) + 1.


21



1, 3, 5, 6, 8, 9, 10, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 84, 85, 86
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OFFSET

0,2


COMMENTS

a(0)=1, a(1)=3; for n>1, a(n)=a(n1)+1 if n is already in the sequence, a(n)=a(n1)+2 otherwise.
Sequence (without first term) is the complement of A000124 (central polygonal numbers).  Jaroslav Krizek, Jun 16 2009


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000
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, arXiv:math/0305308 [math.NT], 2003.


FORMULA

a(n) = A003057(n+1) + n.  Jaroslav Krizek, Jun 16 2009


MATHEMATICA

Table[(n + Round[Sqrt[2 n]] + 1), {n, 0, 80}] (* Vincenzo Librandi, Jan 20 2015 *)


PROG

(PARI) A080036(n)=n+round(sqrt(2*n))+1 \\ M. F. Hasler, Jan 13 2015
(MAGMA) [n + Round(Sqrt(2*n)) + 1: n in [0..80]]; // Vincenzo Librandi, Jan 20 2015


CROSSREFS

Equals A014132 + 1. Cf. A080037.
Different from A105206.
Sequence in context: A175966 A121882 A105206 * A242535 A165290 A026430
Adjacent sequences: A080033 A080034 A080035 * A080037 A080038 A080039


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Mar 14 2003


STATUS

approved



