A001191 - OEIS (original) (raw)

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, 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, 9, 7, 8, 4, 8, 4, 1, 9, 0, 0

COMMENTS

Besicovitch shows that 0.149162536..., this sequence interpreted as a constant, is 10-normal. - Charles R Greathouse IV, Oct 04 2008

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

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

REFERENCES

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.

MATHEMATICA

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 *)

Flatten[IntegerDigits/@(Range[30]^2)] (* Harvey P. Dale, Aug 14 2014 *)

AUTHOR

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