A128849 Denominators of the continued fraction convergents of the decimal concatenation of the twin prime pairs.

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

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 A185895 A358651 * 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