The On-Line Encyclopedia of Integer Sequences® (OEIS®)

The OEIS is supported by the many generous donors to the OEIS Foundation.

Revision History for A014306

(Underlined text is an addition; strikethrough text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A014306

a(n) = 0 if n of form m(m+1)(m+2)/6, otherwise 1.
(history; published version)

#15 by N. J. A. Sloane at Fri Oct 05 11:17:15 EDT 2018

STATUS

proposed

approved

#14 by Antti Karttunen at Mon Oct 01 15:25:04 EDT 2018

STATUS

editing

proposed

Discussion
Mon Oct 01	15:44	David A. Corneth: Ah, I thought you'd left it in editing.

#13 by David A. Corneth at Mon Oct 01 06:49:13 EDT 2018

EXAMPLE

From David A. Corneth, Oct 01 2018: (Start)

For n = 0, floor((6*0-1) ^ (1/3)) = -1. binomial(-1 + 2, 3) = n so a(0) = 0.

For n = 10, floor((6*n-1) ^ (1/3)) = 3. binomial(3 + 2, 3) = n so a(10) = 0.

For n = 11, floor((6*n-1) ^ (1/3)) = 3. binomial(3 + 2, 3) != n so a(11) = 1. (End)

PROG

(PARI) first(n) = my(res = vector(n+1, i, 1), ov = nv = [1, 2, 1, 0]); while(nv[4]<=n, res[nv[4]+1] = 0; for(i = 2, 4, nv[i] = ov[i-1] + ov[i]); ov = nv); res \\ David A. Corneth, Oct 01 2018

KEYWORD

nonn,easy,changed

#12 by David A. Corneth at Mon Oct 01 06:44:42 EDT 2018

PROG

(PARI) a(n) = if(n==0, return(0)); my(t = sqrtnint(6*n-1, 3)); binomial(t+2, 3) != n \\ David A. Corneth, Oct 01 2018

STATUS

proposed

editing

#11 by Antti Karttunen at Sun Sep 30 21:54:37 EDT 2018

STATUS

editing

proposed

Discussion
Mon Oct 01	01:17	Michel Marcus: since you are here , did you try formula by Mikael Aaltonen in A023533? it did not work for me
	06:28	David A. Corneth: a(n) = if(n==0, return(0)); my(t = sqrtnint(6*n-1, 3)); binomial(t+2, 3) != n
	06:44	David A. Corneth: first(n)=my(res=vector(n+1,i,1),ov=nv=[1,2,1,0]);while(nv[4]<=n,res[nv[4]+1]=0;for(i=2,4,nv[i]=ov[i-1]+ov[i]);ov=nv);res

#10 by Antti Karttunen at Sun Sep 30 21:32:20 EDT 2018

LINKS

Antti Karttunen, <a href="/A014306/b014306.txt">Table of n, a(n) for n = 0..65537</a>

#9 by Antti Karttunen at Sun Sep 30 21:30:15 EDT 2018

	DATA	`0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0`
	COMMENTS	`a(A145397(n))=1; a(A000292(n))=0; a(n)=1-A023533(n). [From _). - _Reinhard Zumkeller_, Oct 14 2008]` `Characteristic function of A145397.`
	PROG	`(PARI) A014306(n) = { my(k=0); while(binomial(k+2, 3)<n, k++); !(binomial(k+2, 3)==n); }; \\ Antti Karttunen, Sep 30 2018`
	CROSSREFS	`Cf. A000292, A023533, A145397.`
	EXTENSIONS	`Data section extended up to a(120) by Antti Karttunen, Sep 30 2018`
	STATUS	`approved` `editing`

#8 by Russ Cox at Fri Mar 30 18:55:49 EDT 2012

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu)

Clark Kimberling

Discussion
Fri Mar 30	18:55	OEIS Server: https://oeis.org/edit/global/285

#7 by Russ Cox at Fri Mar 30 18:50:05 EDT 2012

COMMENTS

a(A145397(n))=1; a(A000292(n))=0; a(n)=1-A023533(n). [From _Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Oct 14 2008]

Discussion
Fri Mar 30	18:50	OEIS Server: https://oeis.org/edit/global/246

#6 by Russ Cox at Sun Jul 10 18:18:42 EDT 2011

LINKS

<a href="/Sindx_index/Ch.html#char_fns">Index entries for characteristic functions</a>

Discussion
Sun Jul 10	18:18	OEIS Server: https://oeis.org/edit/global/28

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 18 07:06 EDT 2024. Contains 375255 sequences. (Running on oeis4.)