A130818 Decimal expansion of number whose Engel expansion is the sequence of squares, that is, 1, 4, 9, 16,...

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

Offset: 1

Author

Stephen Casey (hexomino(AT)gmail.com), Jul 17 2007

Keywords

• cons
• easy
• nonn

Examples

			1.2795853023360672674372044408115333532858411...
		

References

• F. Engel "Entwicklung der Zahlen nach Stammbruechen" Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg. pp. 190-191, 1913.

Links

• Stephen Crowley, Two New Zeta Constants: Fractal String, Continued Fraction, and Hypergeometric Aspects of the Riemann Zeta Function, arXiv:1207.1126 [math.NT], 2012, page 17.
• F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.
• Eric Weisstein's World of Mathematics, Engel Expansion
• Eric Weisstein's World of Mathematics, Modified Bessel Function of the First Kind

Crossrefs

Cf. A006784, A064648, A101689.

Programs

Mathematica

RealDigits[BesselI[0, 2] - 1, 10, 105] // First (* Jean-François Alcover, Oct 01 2013 *)

PARI

besseli(0,2)-1 \\ Charles R Greathouse IV, Oct 01 2013

Formula

Equal to Sum_{n>=1} 1/n!^2 or BesselI(0,2) - 1. - Gerald McGarvey, Nov 12 2007

Equals A070910 - 1. - R. J. Mathar, Jun 13 2008