|
Search: id:A002260
|
|
|
| A002260 |
|
Integers 1 to k followed by integers 1 to k+1 etc. (a fractal sequence). |
|
+0
83
|
|
| 1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 1, 2, 3, 4, 5, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 1, 2, 3
(list; table; graph; listen)
|
|
|
OFFSET
|
1,3
|
|
|
COMMENT
|
Start counting again and again.
This is a "doubly fractal sequence" - see the Franklin T. Adams-Watters link.
The PARI functions t1, t2 can be used to read a square array T(n,k) (n >= 1, k >= 1) by antidiagonals downwards: n -> T(t1(n), t2(n)). - Michael Somos, Aug 23, 2002
|
|
REFERENCES
|
Jerry Brown et al., Problem 4619, "School Science and Mathematics", USA, Vol. 97(4), 1997, pp. 221-222.
C. Kimberling, "Numeration systems and fractal sequences," Acta Arithmetica 73 (1995) 103-117.
M. Myers, Smarandache Crescendo Subsequences, R.H.Wilde, An Anthology in Memoriam, Bristol Banner Books, Bristol, 1998, p. 19.
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.
|
|
LINKS
|
N. J. A. Sloane, Table of n, a(n) for n = 1..11325
Franklin T. Adams-Watters, Doubly Fractal Sequences
C. Kimberling, Fractal sequences
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
M. Somos, Sequences used for indexing triangular or square arrays
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
|
|
FORMULA
|
n-th term is n - m(m+1)/2 + 1, where m = [ (sqrt(8n+1) - 1) / 2 ].
a(k * (k + 1) / 2 + i) = i for k >= 0 and 0 < i <= k + 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Aug 14 2001
a(n) = (2 n + round(SQRT(2 n)) - round(SQRT(2 n))^2)/2. E.g. a(47) = 2 - brian tenneson (phoenix(AT)alephnulldimension.net), Oct 11 2003
n+1-binomial(floor((1+sqrt(8n+8))/2), 2). - Paul Barry (pbarry(AT)wit.ie), May 25 2004
T(n,k)=A001511(A118413(n,k)); = T(n,k)=A003602(A118416(n,k)). - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Apr 27 2006
|
|
MAPLE
|
at:=0; for n from 1 to 150 do for i from 1 to n do at:=at+1; lprint(at, i); od: od: - njas, Nov 01 2006
|
|
PROGRAM
|
(PARI) a(n)=n+1-binomial(floor(1/2+sqrt(2+2*n)), 2)
(PARI) t1(n)=n-binomial(floor(1/2+sqrt(2*n)), 2) /* A002260 */
(PARI) t2(n)=binomial(floor(3/2+sqrt(2*n)), 2)-n+1 /* A004736 */
|
|
CROSSREFS
|
A002260(n)=1+A002262(n). Cf. A056534.
Cf. A004736 (ordinal transform), A025581, A002262, A003056.
Adjacent sequences: A002257 A002258 A002259 this_sequence A002261 A002262 A002263
Sequence in context: A113126 A023121 A136261 this_sequence A133994 A066041 A119585
|
|
KEYWORD
|
nonn,easy,nice,tabl
|
|
AUTHOR
|
Angele Hamel (amh(AT)maths.soton.ac.uk)
|
|
EXTENSIONS
|
More terms from Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Apr 27 2006
|
|
|
Search completed in 0.003 seconds
|
