A068995 Integer parts of the square roots of the schizophrenic numbers (A014824).

1, 3, 11, 35, 111, 351, 1111, 3513, 11111, 35136, 111111, 351364, 1111111, 3513641, 11111111, 35136418, 111111111, 351364184, 1111111111, 3513641844, 11111111111, 35136418446, 111111111111, 351364184463, 1111111111111

Offset: 1

Author

Joseph L. Pe, Mar 14 2002

Keywords

• base
• nonn

Comments

a(n) appears to result from (alternately) intermeshing two subsequences, one of the form 11, 111, 1111, ..., the other of the form 35, 351, 3513, .... In both subsequences, the current term is an initial segment of the next term. If the first k (k an even number) terms are deleted from a(n), a(n) can be reconstructed from the resulting sequence by deleting appropriate digits from the end of terms. In this sense, a(n) is self-similar.

Examples

			123 is the third schizophrenic number; its square root has integer part 11.
		

Crossrefs

Cf. A014824.

Programs

Mathematica

h[n_ /; n == 0] := 0; h[n_ /; n > 0] := 10*h[n - 1] + n; t = Table[Floor[Sqrt[h[i]]], {i, 1, 40}]

Formula

From Christopher Hohl, Jun 27 2019: (Start)

a(2n-1) = A014824(n) - A014824(n-1), for n>=1;

a(2n-2) = floor(a(2n-1) / sqrt(10)), for n>=2. (End)