A128846 Numerators of the continued fraction convergents of the decimal concatenation of the upper bounds of twin primes.

0, 1, 1, 4, 745, 749, 1494, 79931, 81425, 242781, 809768, 1052549, 1862317, 28987304, 30849621, 183235409, 214085030, 1467745589, 57456163001, 2058713244234420, 2058770700397421, 30881503049798314, 156466285949388991

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

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

Mathematica

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 *)

Prog

(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", "); ) }

Crossrefs

Sequence in context: A053986 A222961 A160737 * A332174 A195625 A268838

Adjacent sequences: A128843 A128844 A128845 * A128847 A128848 A128849

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 16 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved