A096036 -id:A096036

Search: a096036 -id:a096036

Displaying 1-3 of 3 results found.

page 1

A097052

First occurrence of n in A096036 or 0 if n does not appear.

+20
1

1, 2, 5, 7, 19, 17, 25, 29, 0, 73, 65, 67, 99, 97, 113, 121, 0, 0, 301, 289, 0, 257, 265, 277, 393, 401, 421, 385, 451, 449, 481, 497, 0, 0, 0, 0, 0, 1201, 1161, 1153, 0, 0, 1025, 1033, 1059, 1057, 1105, 1129, 0, 1569, 1613, 1601, 1681, 1697, 1537, 1541, 1801, 1825

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Not appearing in A096036 are 9, 17, 18, 21, 33, 34, 35, 36, 37, 41, 42, 49, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 77, 81, 82, 83, 84, 85, 97, 98, 105, ...,.

LINKS

Table of n, a(n) for n=1..58.

FORMULA

A096036: a(n)= ceiling(n/a(ceiling(n/2))) with a(1) = 1.

MATHEMATICA

a[1] = 1; a[n_] := a[n] = Ceiling[ n / a[ Ceiling[n/2]]]; t = Table[ a[n], {n, 2000}]; b[n_] := Block[{p = Position[t, n, 1, 1]}, If[p == {}, 0, p]]; Flatten[ Table[ b[n], {n, 60}]]

CROSSREFS

Cf. A096036.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller and Robert G. Wilson v, Jul 21 2004

STATUS

approved

A097051

a(n) = floor(n/a(floor(n/2))); a(1) = 1.

+10
5

1, 2, 3, 2, 2, 2, 2, 4, 4, 5, 5, 6, 6, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

If floor(log_2(n))=2k+1, then a(n) = floor(n/2^k). If floor(log_2(n))=2k, then a(n) = 2^k.

EXAMPLE

a(50)=floor(50/a(25))

..... a(25)=floor(25/a(12))

........... a(12)=floor(12/a(6))

................. a(6)=floor(6/a(3))

...................... a(3)=floor(3/a(1))

........................... a(1)=1

...................... a(3)=floor(3/a(1))=floor(3/1)=3

................. a(6)=floor(6/a(3))=floor(6/3)=2

........... a(12)=floor(12/a(6))=floor(12/2)=6

..... a(25)=floor(25/a(12))=floor(25/6)=4

a(50)=floor(50/a(25))=floor(50/4)=12.

MAPLE

f:= proc(n) option remember; floor(n/procname(floor(n/2))) end proc:

f(1):= 1:

map(f, [$1..200]); # Robert Israel, Jan 06 2021

MATHEMATICA

a[1] = 1; a[n_] := a[n] = Floor[n/a[Floor[n/2]]]; Table[ a[n], {n, 94}]

CROSSREFS

Cf. A096036, A097053.

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller and Robert G. Wilson v, Jul 21 2004

EXTENSIONS

Formula added by Max Alekseyev, Mar 02 2011

STATUS

approved

A096038

Triangle T(n,m) = (3*n^2-3*m^2+5*m-4+n)/2 read by rows.

+10
4

1, 6, 4, 14, 12, 7, 25, 23, 18, 10, 39, 37, 32, 24, 13, 56, 54, 49, 41, 30, 16, 76, 74, 69, 61, 50, 36, 19, 99, 97, 92, 84, 73, 59, 42, 22, 125, 123, 118, 110, 99, 85, 68, 48, 25, 154, 152, 147, 139, 128, 114, 97, 77, 54, 28, 186, 184, 179, 171, 160, 146, 129, 109, 86, 60, 31

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

The triangle is obtained by subtracting the triangle A094930 from

its square root (also described in A094930) and then dividing each element of column m through 3*m-1.

For the first three rows n=1 to 3 this yields for example:

4;.................2;............2......................1;

14,25;......minus..2,5;.......=..12,20;......->.divide..6,4;

30,65,64;..........2,5,8;........28,60,56;..............14;12,7;

LINKS

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

FORMULA

T(n,1) = A095794(n).

T(n,n) = 3*n-2.

T(n,m) = A094930(n,m)/(3*m-1)-1.

PROG

(Python)

def A096038(n, m):

return (3*n**2-3*m**2+5*m-4+n)//2

print( [A096038(n, m) for n in range(20) for m in range(1, n+1)] )

# R. J. Mathar, Oct 11 2009

CROSSREFS

Cf. A095794, A011379, A002411, A096037, A096036, A024212.

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Jun 17 2004

EXTENSIONS

Edited, T(3,2) corrected, and extended by R. J. Mathar, Oct 11 2009

STATUS

approved

page 1

Search completed in 0.005 seconds