

A186348


Adjusted joint rank sequence of (f(i)) and (g(j)) with f(i) after g(j) when f(i)=g(j), where f(i)=8i and g(j)=j^2. Complement of A186349.


4



3, 6, 7, 9, 11, 12, 14, 16, 17, 18, 20, 21, 23, 24, 25, 27, 28, 30, 31, 32, 33, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 70, 71, 72, 73, 74, 75, 77, 78, 79, 80, 81, 83, 84, 85, 86, 87, 88
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..66.


FORMULA

a(n) = n+floor(sqrt(8n)).


EXAMPLE

First, write
....8....16..24..32..40..48..56..64..72..80.. (8i)
1..4..9..16...25...36......49....64.......81 (squares)
Then replace each number by its rank, where ties are settled by ranking 8i after the square:
p=(3,6,7,9,11,12,14,16,17,..)=A186348=a(n).
q=(1,2,4,5,8,10,13,15,19,...)=A186349=n+floor((n^21)/8).


MATHEMATICA

(* adjusted joint rank sequences p and q, using general formula for ranking 1st degree u*n+v and 2nd degree x*n^2+y*n+z *)
d=1/2; u=8; v=0; x=1; y=0;
h[n_]:=(y+(4x(u*n+vd)+y^2)^(1/2))/(2x);
a[n_]:=n+Floor[h[n]];
Table[a[n], {n, 1, 120}] (* A186348 *)


PROG

(PARI) a(n)=n+sqrtint(8*n) \\ Charles R Greathouse IV, Jul 05 2013


CROSSREFS

Cf. A186346, A186347, A186349.
Sequence in context: A176237 A187811 A324696 * A071822 A268380 A268378
Adjacent sequences: A186345 A186346 A186347 * A186349 A186350 A186351


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Feb 20 2011


STATUS

approved



