A128850 Numerators of the continued fraction convergents of the decimal concatenation of the prime-indexed primes.

0, 1, 1, 6, 7, 13, 33, 46, 79, 204, 283, 487, 770, 1257, 22139, 23396, 45535, 68931, 183397, 252328, 940381, 3073471, 7087323, 24335440, 153099963, 330535366, 3458453623, 3788988989, 7247442612, 11036431601, 29320305814, 274919183927

Offset

0,4

Comments

Prime-indexed primes (pips) or primeth primes 3, 5, 11, 17, 31, 41, 59, 67, ... are concatenated and then preceded by a decimal point to create the fraction N = .35111731415967... 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.

Links

Table of n, a(n) for n=0..31.

Prog

(PARI) cattpips(n) = { a="."; forprime(x=2, n, a=concat(a, prime(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(numer", "); ) }

Crossrefs

Cf. A006450, A128851 (denominators).

Sequence in context: A160825 A020689 A128844 * A042025 A041072 A154741

Adjacent sequences: A128847 A128848 A128849 * A128851 A128852 A128853

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 16 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved