A128848 Numerators of the continued fraction convergents of the decimal concatenation of the twin prime pairs.

0, 1, 1, 5, 16, 37, 53, 355, 1118, 3709, 8536, 12245, 204456, 421157, 1467927, 1889084, 5246095, 7135179, 12381274, 93804097, 106185371, 306174839, 412360210, 718535049, 1130895259, 2980325567, 16032523094, 35045371755

Offset

0,4

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

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(numer", "); ) }

Crossrefs

Sequence in context: A211806 A001210 A264552 * A274248 A188427 A022496

Adjacent sequences: A128845 A128846 A128847 * A128849 A128850 A128851

Keyword

frac,nonn,base

Author

Cino Hilliard, Apr 16 2007

Extensions

Edited by Charles R Greathouse IV, Apr 25 2010

Status

approved