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A023532 a(n) = 0 if n of form m(m+3)/2, otherwise 1. 57
0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 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, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

From Stark: "alpha = 0.101101110111101111101111110 ... is irrational. For if alpha were rational, its decimal expansion would be periodic and have a period of length r starting with the k-th digit of the expansion.

"But by the very nature of alpha, there will be blocks of r digits, all 1, in this expansion after the k-th digit and the periodicity would then guarantee that everything after such a block of r digits would also be all ones.

"This contradicts the fact that there will always be zeros occurring after any given point in the expansion of alpha. Hence alpha is irrational."

a(A000096(n)) = 0; a(A007401(n)) = 1. - Reinhard Zumkeller, Dec 04 2012

Sequence B is called a reverse reluctant sequence of sequence A, if B is triangle array read by rows: row number k lists first k elements of the sequence A in reverse order. A023532 is reverse reluctant sequence of sequence A211666. - Boris Putievskiy, Jan 11 2013

An example of a sequence with infinite critical exponent [Vaslet]. - N. J. A. Sloane, May 05 2013

REFERENCES

Harold M. Stark, An Introduction to Number Theory, The MIT Press, Cambridge, Mass, eighth printing 1994, page 170.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Boris Putievskiy, Transformations Integer Sequences And Pairing Functions arXiv:1212.2732 [math.CO], 2012.

Elise Vaslet, Critical exponents of words over 3 letters, Electronic Journal of Combinatorics, 18 (2011), #P125.

Index entries for characteristic functions

FORMULA

a(n) = 0 if and only if 8n+9 is a square. [Charles R Greathouse IV, Jun 16 2011]

Blocks of lengths 1, 2, 3, 4, ... ones separated by a single zero.

a(n) = mod(floor(((10^(n+2)-10)/9)10^(n+1-binomial(floor((1+sqrt(9+8n))/2), 2)- (1+floor(log((10^(n+2)-10)/9, 10))))), 10). - Paul Barry, May 25 2004

a(n) = 1-floor((sqrt(9+8n)-1)/2)+floor((sqrt(1+8n)-1)/2). - Paul Barry, May 25 2004

a(n) = A211666(m), where m=(t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). - Boris Putievskiy, Jan 11 2013

EXAMPLE

The start of the sequence as triangle array read by rows:

0;

1,0;

1,1,0;

1,1,1,0;

1,1,1,1,0;

1,1,1,1,1,0;

1,1,1,1,1,1,0;

. . .

- Boris Putievskiy, Jan 11 2013

MATHEMATICA

a = {}; Do[a = Append[a, Join[ {0}, Table[1, {n} ] ] ], {n, 1, 13} ]; a = Flatten[a]

PROG

(PARI) for(n=1, 9, print1("0, "); for(i=1, n, print1("1, "))) \\ Charles R Greathouse IV, Jun 16 2011

(PARI) a(n)=!issquare(8*n+9) \\ Charles R Greathouse IV, Jun 16 2011

(Haskell)

a023532 = (1 -) . a010052 . (+ 9) . (* 8)

a023532_list = concat $ iterate (\rs -> 1 : rs) [0]

-- Reinhard Zumkeller, Dec 04 2012

CROSSREFS

Cf. A023531, A211666.

Sequence in context: A123640 A022924 A157412 * A030308 A280237 A259044

Adjacent sequences:  A023529 A023530 A023531 * A023533 A023534 A023535

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Additional comments from Robert G. Wilson v, Nov 06 2000

STATUS

approved

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Last modified February 23 09:32 EST 2018. Contains 299509 sequences. (Running on oeis4.)