A264934 Decimal expansion of number with continued fraction expansion 0, 1, 11, 111, 1111, 11111 ... (the repunits).

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

Offset: 0

Author

Ilya Gutkovskiy, Nov 28 2015

Keywords

• nonn
• cons

Examples

			0.91672918178902416365663076735032501895175899962194272298… = 0 + 1/(1 + 1/(11 + 1/(111 + 1/(1111 + 1/(11111 + 1/(111111 + 1/(1111111 + 1/(11111111 + 1/...)))))))).
		

Links

• Eric Weisstein's World of Mathematics, Repunit

Crossrefs

Cf. A002275.

Programs

Mathematica

RealDigits@ N[FromContinuedFraction@ Prepend[Table[FromDigits@ Table[1, {n}], {n, 30}], 0], 110] // First (* Michael De Vlieger, Nov 28 2015 *)

Formula

Approximation: ~ -zeta(1/2) - sqrt(5)*exp(-sqrt(2)).