This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A269805 #16 Nov 05 2018 21:23:14 %S A269805 5,10,15,20,30,37,40,43,45,59,60,61,73,74,80,85,86,90,97,101,103,107, %T A269805 111,118,120,122,127,129,135,139,146,148,160,167,170,172,177,180,183, %U A269805 194,199,202,206,214,219,222,236,240,244,254,255,258,270,277,278,291 %N A269805 Numbers having harmonic fractility A270000(n) = 2. %C A269805 In order to define (harmonic) fractility of an integer n > 1, we first define nested interval sequences. Suppose that r = (r(n)) is a sequence satisfying (i) 1 = r(1) > r(2) > r(3) > ... and (ii) r(n) -> 0. For x in (0,1], let n(1) be the index n such that r(n+1) < x <= r(n), and let L(1) = r(n(1))-r(n(1)+1). Let n(2) be the largest index n such that x <= r(n(1)+1) + L(1)*r(n), and let L(2) = (r(n(2))-r(n(2)+1))*L(1). Continue inductively to obtain the sequence (n(1), n(2), n(3), ... ) =: NI(x), the r-nested interval sequence of x. %C A269805 For fixed r, call x and y equivalent if NI(x) and NI(y) are eventually equal (up to an offset). For n > 1, the r-fractility of n is the number of equivalence classes of sequences NI(m/n) for 0 < m < n. Taking r = (1/1, 1/2, 1/3, 1/4, ...) gives harmonic fractility. %H A269805 Jack W Grahl, <a href="/A269805/b269805.txt">Table of n, a(n) for n = 1..189</a> %e A269805 Nested interval sequences NI(k/m) for m = 5: %e A269805 NI(1/5) = (5, 1, 1, 1, 1, 1,...), %e A269805 NI(2/5) = (2, 2, 2, 2, 2, 2,...), %e A269805 NI(3/5) = (1, 5, 1, 1, 1, 1,...), %e A269805 NI(4/5) = (1, 1, 5, 1, 1, 1,...), %e A269805 so that there are 2 equivalence classes for n = 5, and the fractility of 5 is 2. %o A269805 (PARI) select( is_A269805(m)=A270000(n)==2, [1..300]) \\ _M. F. Hasler_, Nov 05 2018 %Y A269805 Cf. A269804, A269806, A269807, A269808, A269809 (numbers with harmonic fractility 1, 3, ..., 6), A270000 (harmonic fractility of n). %K A269805 nonn,easy %O A269805 1,1 %A A269805 _Clark Kimberling_ and _Peter J. C. Moses_, Mar 05 2016 %E A269805 Edited by _M. F. Hasler_, Nov 05 2018