The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A265776 Numerators of primes-only best approximates (POBAs) to sqrt(2); see Comments. 7
 2, 3, 7, 41, 977, 1093, 1373, 1427, 3701, 8597, 22247, 38287, 53569, 61927, 78643 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Suppose that x > 0. A fraction p/q of primes is a primes-only best approximate (POBA), and we write "p/q in B(x)", if 0 < |x - p/q| < |x - u/v| for all primes u and v such that v < q, and also, |x - p/q| < |x - p'/q| for every prime p' except p. Note that for some choices of x, there are values of q for which there are two POBAs. In these cases, the greater is placed first; e.g., B(3) = (7/2, 5/2, 17/5, 13/5, 23/7, 19/7, ...). See A265759 for a guide to related sequences. LINKS EXAMPLE The POBAs to sqrt(2) start with 2/2, 3/2, 7/5, 41/29, 977/691, 1093/773, 1373/971, 1427/1009. For example, if p and q are primes and q > 29, then 41/29 is closer to sqrt(2) than p/q is. MATHEMATICA x = Sqrt[2]; z = 800; p[k_] := p[k] = Prime[k]; t = Table[Max[Table[NextPrime[x*p[k], -1]/p[k], {k, 1, n}]], {n, 1, z}]; d = DeleteDuplicates[t]; tL = Select[d, # > 0 &] (* lower POBA *) t = Table[Min[Table[NextPrime[x*p[k]]/p[k], {k, 1, n}]], {n, 1, z}]; d = DeleteDuplicates[t]; tU = Select[d, # > 0 &] (* upper POBA *) v = Sort[Union[tL, tU], Abs[#1 - x] > Abs[#2 - x] &]; b = Denominator[v]; s = Select[Range[Length[b]], b[[#]] == Min[Drop[b, # - 1]] &]; y = Table[v[[s[[n]]]], {n, 1, Length[s]}] (* POBA, A265776/A265777 *) Numerator[tL]   (* A265772 *) Denominator[tL] (* A265773 *) Numerator[tU]   (* A265774 *) Denominator[tU] (* A265775 *) Numerator[y]    (* A265776 *) Denominator[y]  (* A265777 *) CROSSREFS Cf. A000040, A265759, A265772, A265773, A265774, A265775, A265777. Sequence in context: A037843 A102604 A119662 * A163157 A260819 A000945 Adjacent sequences:  A265773 A265774 A265775 * A265777 A265778 A265779 KEYWORD nonn,frac,more AUTHOR Clark Kimberling, Dec 20 2015 EXTENSIONS a(11)-a(15) from Robert Price, Apr 05 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 25 23:44 EST 2020. Contains 332270 sequences. (Running on oeis4.)