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A014306 a(n) = 0 if n of form m(m+1)(m+2)/6, otherwise 1. 38
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(A145397(n))=1; a(A000292(n))=0; a(n)=1-A023533(n). - Reinhard Zumkeller, Oct 14 2008

Characteristic function of A145397.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

Index entries for characteristic functions

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) A014306(n) = { my(k=0); while(binomial(k+2, 3)<n, k++); !(binomial(k+2, 3)==n); }; \\ Antti Karttunen, Sep 30 2018

(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

(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

CROSSREFS

Cf. A000292, A023533, A145397.

Sequence in context: A126564 A180433 A165560 * A138150 A271591 A287790

Adjacent sequences:  A014303 A014304 A014305 * A014307 A014308 A014309

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Data section extended up to a(120) by Antti Karttunen, Sep 30 2018

STATUS

approved

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Last modified January 19 03:18 EST 2019. Contains 319282 sequences. (Running on oeis4.)