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A128849 Denominators of the continued fraction convergents of the decimal concatenation of the twin prime pairs. 0
1, 2, 3, 14, 45, 104, 149, 998, 3143, 10427, 23997, 34424, 574781, 1183986, 4126739, 5310725, 14748189, 20058914, 34807103, 263708635, 298515738, 860740111, 1159255849, 2019995960, 3179251809, 8378499578, 45071749699, 98521998976 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

FORMULA

The twin prime pairs 3,5,5,7,11,13,17,19... are concatenated and then preceded by a decimal point to create the fraction N = .3557111317192931... 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

With[{c=FromDigits[Flatten[IntegerDigits/@Flatten[Select[Partition[Prime[Range[ 200]], 2, 1], #[[2]]-#[[1]]==2&]]]]}, Take[Denominator[Convergents[ N[ c/10^IntegerLength[c], IntegerLength[c]]]], 40]] (* Harvey P. Dale, Nov 11 2013 *)

PROG

(PARI) cattwinP(n) = { a="."; forprime(x=3, n, if(ispseudoprime(x+2), a=concat(a, Str(x)); 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: A281486 A047067 A185895 * A294495 A188289 A153741

Adjacent sequences:  A128846 A128847 A128848 * A128850 A128851 A128852

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 July 5 07:44 EDT 2020. Contains 335462 sequences. (Running on oeis4.)