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A214032
Places n where A214030(n) = n-2.
2
17, 67, 109, 137, 181, 191, 229, 233, 239, 257, 283, 307, 311, 349, 353, 359, 479, 523, 547, 593, 599, 617, 643, 709, 719, 829, 839, 657, 883, 907, 911, 953, 977, 1021, 1031, 1069, 1097, 1123, 1151, 1193, 1217, 1319, 1433, 1439, 1483
OFFSET
1,1
COMMENTS
This sequence is to A214030 as A000057 is to A001177. It would be nice to have an interpretation of this sequence akin to the interpretation of A000057 as the set of primes which divide all Fibonacci sequences, having arbitrary initial values for a(1),a(2). The linearly recursive sequence which seems to be associated to this is 3*f(n)=6*f(n-1)+2*f(n-2), but this does not have integral values.
If we use the sequence 3,2,3,2,3,2.. instead of 2,3,2,3,... we end up with the same sequence a(n).
PROG
(PARI)
{b23(n)=local(t, m=1, s=[n]); if (n<2, 0, while(1,
if(m%2, s=concat(s, 2), s=concat(s, 3));
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 the sequence A214032(n) to the screen, */
for(i=1, 1500, if(b23(i)==i-2, print1(i, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Art DuPre, Jul 12 2012
STATUS
approved