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

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..60.

Prog

(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]<n^2||t[#t]<n^2, m++, break)); m)};
//To print out the sequence A214034//
for(i=2, 70, print1(a24(i), ", "))

Crossrefs

Cf. A214030.

Sequence in context: A086786 A211890 A231406 * A343224 A047844 A081217

Adjacent sequences: A214031 A214032 A214033 * A214035 A214036 A214037

Keyword

nonn

Author

Art DuPre, Jul 21 2012

Status

approved