A242403 Decimal expansion of the binary self-numbers density constant.

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

Offset

0,1

Comments

This constant is transcendental (Troi and Zannier, 1999). - Amiram Eldar, Nov 28 2020

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 179.

József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 4, p. 384-386.

G. Troi and U. Zannier, Note on the density constant in the distribution of self-numbers, Bollettino dell'Unione Matematica Italiana, Serie 7, Vol. 9-A, No. 1 (1995), pp. 143-148.

Links

Table of n, a(n) for n=0..99.

G. Troi and U. Zannier, Note on the density constant in the distribution of self-numbers - II, Bollettino dell'Unione Matematica Italiana, Serie 8, Vol. 2-B, No. 2 (1999), pp. 397-399; alternative link.

Umberto Zannier, On the distribution of self-numbers, Proc. Amer. Math. Soc., Vol. 85, No. 1 (1982), pp. 10-14.

Index entries for transcendental numbers

Formula

Equals (1/8)*(Sum_{n not a binary self-number} 1/2^n)^2.

Example

0.2526602590088829221550627143278941418252...

Mathematica

m0 = 100; dm = 100; digits = 100; Clear[lambda]; lambda[m_] := lambda[m] = Total[1/2^Union[Table[n + Total[IntegerDigits[n, 2]], {n, 0, m}]]]^2/8 // N[#, 2*digits]& // RealDigits[#, 10, 2*digits]& // First; lambda[m0]; lambda[m = m0 + dm]; While[lambda[m] != lambda[m - dm], Print["m = ", m]; m = m + dm]; lambda[m][[1 ;; digits]]

Crossrefs

Cf. A010061 (binary self numbers), A003052 (decimal self numbers), A010064, A010067, A010070, A092391, A228082.

Sequence in context: A344077 A198539 A121311 * A179015 A195621 A267090

Adjacent sequences: A242400 A242401 A242402 * A242404 A242405 A242406

Keyword

nonn,cons

Author

Jean-François Alcover, May 13 2014

Status

approved