A128845 Denominators of the continued fraction convergents of the decimal concatenation of the lower bound of twin primes.

1, 2, 3, 17, 20, 37, 94, 131, 225, 581, 806, 1387, 2193, 3580, 9353, 12933, 22286, 35219, 57505, 1472844, 1530349, 50444012, 102418373, 255280758, 30480828575, 152659423633, 1251756217639, 1404415641272, 2656171858911, 6716759359094

Offset

0,2

Links

Table of n, a(n) for n=0..29.

Formula

The lower bounds of twin primes 3,5,11,17... are concatenated and then preceded by a decimal point to create the fraction N = .35111729... . 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

Prog

(PARI) cattwinsL(n) = a="."; forprime(x=3, n, if(ispseudoprime(x+2), a=concat(a, Str(x)))); 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", "); ) }

Crossrefs

Sequence in context: A140834 A121409 A041295 * A128851 A078737 A041981

Adjacent sequences: A128842 A128843 A128844 * A128846 A128847 A128848

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 16 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved