A346190 Decimal expansion of Sum_{k>=0} 1/(2^(2^(2*k+1)) - 1).

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

Offset: 0

Author

Amiram Eldar, Jul 09 2021

Keywords

• nonn
• cons

Comments

This constant is transcendental (Schwarz, 1967).

Examples

			0.50781250046566128730773925781250000000587747175411...
		

Links

• Wolfgang Schwarz, Remarks on the irrationality and transcendence of certain series, Mathematica Scandinavica, Vol. 20, No. 2 (1967), pp. 269-274; alternative link.
• Index entries for transcendental numbers

Crossrefs

Cf. A048649, A076214, A346191, A346192.

Programs

Mathematica

RealDigits[Sum[1/(2^(2^(2*n + 1) - 1)), {n, 0, 10}], 10, 100][[1]]

Formula

Equals A076214 - A346191.