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%I #6 Nov 11 2013 11:36:28
%S 1,2,3,14,45,104,149,998,3143,10427,23997,34424,574781,1183986,
%T 4126739,5310725,14748189,20058914,34807103,263708635,298515738,
%U 860740111,1159255849,2019995960,3179251809,8378499578,45071749699,98521998976
%N Denominators of the continued fraction convergents of the decimal concatenation of the twin prime pairs.
%F The twin prime pairs 3,5,5,7,11,13,17,19... are concatenated and then preceded by a decimal point to create the fraction N = .3557111317192931... 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 With[{c=FromDigits[Flatten[IntegerDigits/@Flatten[Select[Partition[Prime[Range[ 200]],2,1], #[[2]]-#[[1]]==2&]]]]},Take[Denominator[Convergents[ N[ c/10^IntegerLength[c],IntegerLength[c]]]],40]] (* _Harvey P. Dale_, Nov 11 2013 *)
%o (PARI) cattwinP(n) = { a=".";forprime(x=3,n,if(ispseudoprime(x+2),a=concat(a,Str(x)); 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(denom","); ) }
%K frac,nonn,base
%O 0,2
%A _Cino Hilliard_, Apr 16 2007
%E Edited by _Charles R Greathouse IV_, Apr 25 2010
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