A128847 Denominators of the continued fraction convergents of the decimal concatenation of the upper bounds of twin primes.

1, 1, 2, 7, 1304, 1311, 2615, 139906, 142521, 424948, 1417365, 1842313, 3259678, 50737483, 53997161, 320723288, 374720449, 2569045982, 100567513747, 3603437154114739, 3603537721628486, 54052965256913543, 273868364006196201

Offset

0,3

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

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(denom", "); ) }

Crossrefs

Sequence in context: A056165 A082891 A000653 * A123180 A138198 A358482

Adjacent sequences: A128844 A128845 A128846 * A128848 A128849 A128850

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 16 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved