

A118011


Complement of the Connell sequence (A001614); a(n) = 4*n  A001614(n).


4



3, 6, 8, 11, 13, 15, 18, 20, 22, 24, 27, 29, 31, 33, 35, 38, 40, 42, 44, 46, 48, 51, 53, 55, 57, 59, 61, 63, 66, 68, 70, 72, 74, 76, 78, 80, 83, 85, 87, 89, 91, 93, 95, 97, 99, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 123, 125, 127, 129, 131, 133, 135, 137, 139
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

a(n) is the position of the second appearance of n in A117384, where A117384(m) = A117384(k) and k = 4*A117384(m)  m. The Connell sequence (A001614) is generated as: 1 odd, 2 even, 3 odd, ...


LINKS

Table of n, a(n) for n=1..64.


FORMULA

A001614(n) = A118012(a(n)).
a(n) = 2n+[(1+sqrt(8n7))/2].  JuriStepan Gerasimov Aug 25 2009
a(n) = 2*n+round(sqrt(2*n)).  Gerald Hillier, Apr 16 2015
From Robert Israel, Apr 20 2015 (Start):
a(n) = 2*n + 1 + Sum(j=0 .. n2, A023531(j)).
G.f. 2*x/(1x)^2 + x/(1x) * Sum(j=0..infinity, x^(j*(j+1)/2))
= 2*x/(1x)^2 + x^(7/8)/(22*x) * Theta2(0,sqrt(x)), where Theta2 is a Jacobi theta function. (End)


MATHEMATICA

Table[2 n + Round[Sqrt[2 n]], {n, 70}] (* Vincenzo Librandi, Apr 16 2015 *)


PROG

(MAGMA) [2*n+Round(Sqrt(2*n)): n in [1..70]]; // Vincenzo Librandi, Apr 16 2015


CROSSREFS

Cf. A001614, A023531, A117384, A118012.
A171152 gives partial sums.
Sequence in context: A140482 A212451 A244223 * A189679 A190229 A190085
Adjacent sequences: A118008 A118009 A118010 * A118012 A118013 A118014


KEYWORD

nonn


AUTHOR

Paul D. Hanna, Apr 10 2006


STATUS

approved



