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

1,2

Links

Table of n, a(n) for n=1..27.

H. T. Freitag and G. M. Phillips, Sylvester's algorithm and Fibonacci numbers, in Applications of Fibonacci numbers, Vol. 8, 155-163, Springer, Dordrecht, 1999.

Formula

a(n) == 1 (mod n). - Pontus von Brömssen, Apr 25 2026

Example

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

Prog

(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)

Crossrefs

Sequence in context: A364189 A099983 A275631 * A233930 A292447 A176690

Adjacent sequences: A048857 A048858 A048859 * A048861 A048862 A048863

Keyword

nonn,more

Author

Jeffrey Shallit, Jul 04 2000

Extensions

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

Status

approved