%I #8 Nov 21 2013 12:49:03

%S 0,1,1,4,745,749,1494,79931,81425,242781,809768,1052549,1862317,

%T 28987304,30849621,183235409,214085030,1467745589,57456163001,

%U 2058713244234420,2058770700397421,30881503049798314,156466285949388991

%N Numerators of the continued fraction convergents of the decimal concatenation of the upper bounds of twin primes.

%F The upper bounds of twin primes 5,7,13,19... are concatenated and then preceded by a decimal point to create the fraction N = .57131931... . This number is then evaluated with n=0,m=steps to iterate,x = N, a(0)=floor(N) using the loop: do a(n)=floor(x) x=1/(x-a(n)) n=n+1 loop until n=m

%t x=(FromDigits[Flatten[IntegerDigits[#]&/@(Transpose[Select[ Partition[ Prime[Range[200]],2,1],Last[#]-First[#]==2&]][[2]])]]); Numerator/@ Convergents[N[x/10^IntegerLength[x],100],40] (* _Harvey P. Dale_, May 11 2011 *)

%o (PARI) cattwinsU(n) = { a=".";forprime(x=3,n,if(ispseudoprime(x+2),a=concat(a,Str(x+2))));a=eval(a) } cfrac2(m,f) = { default(realprecision,1000); cf = vector(m+10); cf = contfrac(f); for(m1=1,m-1, r=cf[m1+1]; forstep(n=m1,1,-1, r = 1/r; r+=cf[n];); numer=numerator(r); denom=denominator(r); print1(numer","); ) }

%K frac,nonn,base

%O 0,4

%A _Cino Hilliard_, Apr 16 2007

%E Edited by _Charles R Greathouse IV_, Apr 25 2010