A214034 The apparition sequence for 2,4 continued fractions.

1, 2, 3, 3, 5, 7, 7, 2, 3, 5, 11, 13, 7, 11, 15, 8, 5, 8, 3, 23, 5, 21, 23, 19, 13, 8, 7, 27, 11, 31, 31, 5, 17, 7, 11, 37, 17, 41, 7, 20, 23, 20, 11, 11, 21, 45, 47, 7, 19, 8, 27, 51, 17, 11, 7, 8, 27, 14, 11, 61, 31, 23, 63, 27, 5, 32, 35, 65, 7, 69, 23, 35, 37, 59, 35, 23, 41, 79, 15

Offset: 1

Author

Art DuPre, Jul 21 2012

Keywords

• nonn

Comments

See A214030 for an explanation. There seems to be no corresponding linear recurrence.

Crossrefs

Cf. A214030.

Programs

PARI

{a24(n)=local(t,m=1,s=[n]);if(n<2,0,while(1,
if(m%2,s=concat(s,2),s=concat(s,4));
t=contfracpnqn(concat(s,n));
t=contfrac(n*t[1,1]/t[2,1]);
if(t[1]A214034 */
for(i=2,70,print1(a24(i),", "))

Extensions

More terms from Michel Marcus, Jan 15 2025