A048860 Smallest denominator d such that the Sylvester expansion of n/d has n terms.

1, 3, 7, 17, 31, 109, 253, 97, 271, 1621, 199, 3961, 1769, 12013, 16381, 3169, 24991, 15877, 180881, 265201, 2620801, 26753, 781219, 14473441, 693551, 55689349, 18294823

Offset: 1

Author

Jeffrey Shallit, Jul 04 2000

Keywords

• nonn

Examples

			a(3) = 7 since 3/7 = 1/3 + 1/11 + 1/231
		

References

• H. T. Freitag and G. M. Phillips, Sylvester's algorithm and Fibonacci numbers, in Applications of Fibonacci numbers, Vol. 8 (Rochester, NY, 1998), 155-163, Kluwer Acad. Publ., Dordrecht, 1999.

Programs

PARI

a(n)=if(n==1,q=1,q=n+1;while(1,c=1;P=n;Q=q;while(Q%P>0,c++;D=Q\P+1;P=P*D-Q;Q*=D);if(c==n,break);q+=n));return(q)

Extensions

a(20)-a(27) from Robert Gerbicz, Nov 19 2010