A214033 Places n where A214030(n) = n or A214030(n) = n-2.

13, 17, 19, 23, 37, 41, 47, 67, 89, 109, 137, 139, 157, 181, 191, 211, 229, 233, 239, 257, 277, 281, 283, 307, 311, 331, 349, 353, 359, 373, 379, 397, 479, 499, 503, 521, 523, 547, 571, 593, 599, 613, 617, 619, 641

Offset

1,1

Comments

It always has been one of the great mysteries of mathematics, that the superdiagonal sequence of A001177 consists of prime numbers A000057.

Here, regarding A214031 and A214032,there is the further conjecture that these two disjoint sequences are primes and roughly comparable in density. It isn't clear that these two sequences have a density, without appealing to the Riemann Hypothesis, but they are certainly close to one another in growing size.

Since these two sequences are disjoint, it is natural to take their union.

Links

Table of n, a(n) for n=1..45.

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 a(n) to the screen,
for(i=1, 500, if(b23(i)==i||b23(i)==i-2,
print1(i, ", ")));

Crossrefs

Cf. A000057, A001177, A214030-A213032.

Sequence in context: A168447 A191059 A165681 * A268593 A175873 A167802

Adjacent sequences: A214030 A214031 A214032 * A214034 A214035 A214036

Keyword

nonn

Author

Art DuPre, Jul 12 2012

Status

approved