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A083479 The natural numbers with all terms of A033638 inserted. 7
0, 1, 1, 1, 2, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 10, 10, 11, 12, 13, 13, 14, 15, 16, 17, 17, 18, 19, 20, 21, 21, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 31, 31, 32, 33, 34, 35, 36, 37, 37, 38, 39, 40, 41, 42, 43, 43, 44, 45, 46, 47, 48, 49, 50, 50, 51, 52, 53, 54, 55, 56, 57, 57 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row n of A049597 has a(n+1) nonzero values.

When considering the set of nested parabolas defined by -(x^2) + p*x for integer values of p, a(n) tells us how many parabolas are intersected by the line from (1,n) to (n,n). - Gregory R. Bryant, Apr 01 2013

Number of distinct perimeters for polyominos with n square cells. - Wesley Prosser, Sep 06 2017

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = ((n+2)-ceiling(sqrt(4*n))). - Gregory R. Bryant, Apr 01 2013

From Wesley Prosser, Sep 06 2017: (Start)

a(n) = (n+2) - A027709(n)/2.

a(n) = (n+2) - A027434(n).

a(n) = (2n+2) - A049068(n).

a(n) = (2n+3) - A080037(n).

(End)

EXAMPLE

There are three 1's, one from the natural numbers and two from A033638.

When viewed as an array the sequence begins:

0

1

1 1

2 2

3 3 4

5 5 6

7 7 8 9

10 10 11 12

13 13 14 15 16

17 17 18 19 20

21 21 22 23 24 25

26 26 27 28 29 30

...

MATHEMATICA

Table[(n + 2) - Ceiling@ Sqrt[4 n] - 2 Boole[n == 0], {n, 0, 73}] (* Michael De Vlieger, Sep 05 2017 *)

PROG

(Haskell)

a083479 n = a083479_list !! n

a083479_list = m [0..] a033638_list where

   m xs'@(x:xs) ys'@(y:ys) | x <= y    = x : m xs ys'

                           | otherwise = y : m xs' ys

-- Reinhard Zumkeller, Apr 06 2012

(Maxima)

a(n):=((n+2)-ceiling(sqrt(4*n))); /* Gregory R. Bryant, Apr 01 2013 */

CROSSREFS

Cf. A033638, A049597, A054243, A060510.

Cf. A002620, A083480, A083906.

Sequence in context: A248610 A168581 A024699 * A112231 A213856 A173329

Adjacent sequences:  A083476 A083477 A083478 * A083480 A083481 A083482

KEYWORD

easy,nonn,tabf

AUTHOR

Alford Arnold, Jun 08 2003

EXTENSIONS

Edited and extended by David Wasserman, Nov 16 2004

STATUS

approved

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Last modified April 26 09:52 EDT 2019. Contains 322472 sequences. (Running on oeis4.)