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A128850 Numerator of the continued fraction convergents of the decimal concatenation of prime-indexed primes. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Pips of order 1, pips(1) = prime(prime(x)). Pips of order 2, pips(2) = prime(prime(prime(x))) etc.

LINKS

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

FORMULA

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.

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

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

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Last modified June 1 23:14 EDT 2020. Contains 334765 sequences. (Running on oeis4.)