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A128846 Numerators of the continued fraction convergents of the decimal concatenation of the upper bounds of twin primes. 0
0, 1, 1, 4, 745, 749, 1494, 79931, 81425, 242781, 809768, 1052549, 1862317, 28987304, 30849621, 183235409, 214085030, 1467745589, 57456163001, 2058713244234420, 2058770700397421, 30881503049798314, 156466285949388991 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 4 20:00 EDT 2020. Contains 336202 sequences. (Running on oeis4.)