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 A214033 Places n where A214030(n) = n or A214030(n) = n-2. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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 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]

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Last modified January 18 16:27 EST 2020. Contains 331011 sequences. (Running on oeis4.)