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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 (list; graph; refs; listen; history; text; internal format)
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^2-1)/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+v-d)+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

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Last modified April 18 08:37 EDT 2019. Contains 322209 sequences. (Running on oeis4.)