A001191 - OEIS

%I #46 Nov 26 2015 05:54:26

%S 1,4,9,1,6,2,5,3,6,4,9,6,4,8,1,1,0,0,1,2,1,1,4,4,1,6,9,1,9,6,2,2,5,2,

%T 5,6,2,8,9,3,2,4,3,6,1,4,0,0,4,4,1,4,8,4,5,2,9,5,7,6,6,2,5,6,7,6,7,2,

%U 9,7,8,4,8,4,1,9,0,0

%N Digits of positive squares.

%C Besicovitch shows that 0.149162536..., this sequence interpreted as a constant, is 10-normal. - _Charles R Greathouse IV_, Oct 04 2008

%C The continued fraction of this sequence interpreted as a constant (0.149162536...) displays behavior similar to that of Champernowne's constant, with huge coefficients becoming unbounded: the 47th coefficient has 39 digits, the 103rd coefficient has 178 digits, the 289th coefficient is greater than 10^712, etc. - _John M. Campbell_, Jun 25 2011

%C Position of record terms of the continued fraction: 1, 2, 14, 18, 47, 103, 289, 831, 2215, 5801, 14167, 33339, 76595, 174815, 391749, ..., ; Digital length of the record terms: 1, 1, 1, 2, 39, 178, 712, 2637, 9577, 33986, 119198, 413749, 1424714, 4872958, 16572040, ..., . - _Robert G. Wilson v_, Jul 04 2011

%D G. Harman, One hundred years of normal numbers, in M. A. Bennett et al., eds., Number Theory for the Millennium, II (Urbana, IL, 2000), 149-166, A K Peters, Natick, MA, 2002.

%H Vincenzo Librandi, <a href="/A001191/b001191.txt">Table of n, a(n) for n = 1..5500</a>

%H A. S. Besicovitch, <a href="http://dx.doi.org/10.1007/BF01201350">The asymptotic distribution of the numerals in the decimal representation of the squares of the natural numbers</a>, Mathematische Zeitschrift 39 (1934), pp. 146-156.

%H Paul Pollack, Joseph Vandehey, <a href="http://arxiv.org/abs/1405.6266">Besicovitch, Bisection, and the normality of 0.(1)(4)(9)(16)(25)...</a>, arXiv:1405.6266 [math.NT], 2014.

%H Paul Pollack, Joseph Vandehey, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.122.8.757">Besicovitch, Bisection, and the Normality of 0.(1)(4)(9)(16)(25)...</a>, The American Mathematical Monthly 122.8 (2015): 757-765.

%t mx = 30; k = 1; s = 0; While[k < mx+1, s = s (10^IntegerLength[k^2]) + k^2; k++]; IntegerDigits@ s (* _Robert G. Wilson v_, Jul 04 2011 *)

%t Flatten[IntegerDigits/@(Range[30]^2)] (* _Harvey P. Dale_, Aug 14 2014 *)

%K nonn,base,easy

%O 1,2

%A Charlie Peck (peck(AT)Alice.Wonderland.Caltech.EDU)