Part 15

The request was sent by (Mr.) B.J. Mares on Sat Dec 9 19:10:27 PST 1995 The email address is: bjmares@teleport.com

The number to be tested is:

.86224012586805457155779028324939457856576474276829909451607121455730674059051645804203844143861813$ 451257229030330958513908111490904372705631904836799517334609935566864203581911199877725969528883243$

Another binary pattern.

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The request was sent by Jon Borwein on Sun Nov 5 06:09:28 GMT 1995 The email address is: jborwein@cecm.sfu.ca

The number to be tested is: .01118680003287710787004681

The number of correct digits in the number: 20

The test(s) to be performed on the number: algebraic

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1.456791031046907

The number of correct digits in the number: 16

The test(s) to be performed on the number: algebraic gammamultiplicative gammaadditve zetamultiplicative zetaadditive psidigamma lineardependence_salvage

The hints given by the user:

p(0)=1 q(0)=2

p(i+1)=sqrt(p(i)*q(i)) i = 0,1,2,.. q(i+1)=(p(i) + q(i))/2 i = 0,1,2,..

x = lim p(i) = lim q(i) i->+inf i->+inf

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The request was sent by Olivier Gerard on Mon Jan 29 18:48:42 PST 1996 The email address is: quadrature@onco.techlink.fr

The number to be tested is: 1.062550805496255938

This number arises in the study of generalized Zeta functions on non associative sets.

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The request was sent by Michael Mossinghoff on Fri Feb 9 14:40:28 PST 1996 The email address is: mjm@math.appstate.edu

The number to be tested is: 1.296210659593309 (see below for 2500 digits of it).

As I mentioned in the original note, it would be interesting to see if this number satisfies a simple polynomial of degree > 34. The simplest polynomial I know of that it satisfies is

x^38-x^36-x^34-x^29+x^28-x^24-x^14+x^10-x^9-x^4-x^2+1

I found this during a search for polynomials with height 1, degree 38, and Mahler measure < 1.3.

I also have a second new Salem number that would be interesting to try.