

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
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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 A334742 A213856
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



