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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. 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 a(n) = [A002262(n) 1 : rs) [0] -- Reinhard Zumkeller, Dec 04 2012 CROSSREFS Cf. A023531, A211666. Essentially the same sequence as A114607 and A123110. - N. J. A. Sloane, Feb 07 2020 Sequence in context: A022924 A295893 A157412 * A226520 A268921 A327180 Adjacent sequences:  A023529 A023530 A023531 * A023533 A023534 A023535 KEYWORD nonn,easy AUTHOR EXTENSIONS Additional comments from Robert G. Wilson v, Nov 06 2000 STATUS approved

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Last modified August 15 10:12 EDT 2020. Contains 336492 sequences. (Running on oeis4.)