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

%I A130818 #36 Jun 16 2025 12:19:01
%S A130818 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,
%T A130818 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,
%U A130818 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
%N A130818 Decimal expansion of number whose Engel expansion is the sequence of squares, that is, 1, 4, 9, 16,...
%D A130818 F. Engel "Entwicklung der Zahlen nach Stammbruechen" Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg. pp. 190-191, 1913.
%H A130818 Stephen Crowley, <a href="https://arxiv.org/abs/1207.1126">Two New Zeta Constants: Fractal String, Continued Fraction, and Hypergeometric Aspects of the Riemann Zeta Function</a>, arXiv:1207.1126 [math.NT], 2012, page 17.
%H A130818 F. Engel, <a href="/A006784/a006784.pdf">Entwicklung der Zahlen nach Stammbruechen</a>, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.
%H A130818 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>
%H A130818 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ModifiedBesselFunctionoftheFirstKind.html">Modified Bessel Function of the First Kind</a>
%F A130818 Equal to Sum_{n>=1} 1/n!^2 or BesselI(0,2) - 1. - _Gerald McGarvey_, Nov 12 2007
%F A130818 Equals A070910 - 1. - _R. J. Mathar_, Jun 13 2008
%e A130818 1.2795853023360672674372044408115333532858411...
%t A130818 RealDigits[BesselI[0, 2] - 1, 10, 105] // First (* _Jean-François Alcover_, Oct 01 2013 *)
%o A130818 (PARI) besseli(0,2)-1 \\ _Charles R Greathouse IV_, Oct 01 2013
%Y A130818 Cf. A006784, A064648, A101689.
%K A130818 cons,easy,nonn
%O A130818 1,2
%A A130818 Stephen Casey (hexomino(AT)gmail.com), Jul 17 2007