cp's OEIS Frontend

A344007 Denominators of triangle formed by beginning with 1 on row 1, then producing row n by replacing the largest value on row n-1, k, by 1/n and k - 1/n, and arranging the entries in order from smallest to largest.

%I A344007 #46 Jun 09 2021 12:33:46
%S A344007 1,2,2,6,3,2,6,4,4,3,15,6,5,4,4,12,15,6,6,5,4,12,28,15,7,6,6,5,40,12,
%T A344007 28,8,15,7,6,6,18,40,12,28,9,8,15,7,6,18,15,40,12,10,28,9,8,15,7,77,
%U A344007 18,15,40,12,11,10,28,9,8,15,20,77,18,15,40,12,12,11,10,28,9,8
%N A344007 Denominators of triangle formed by beginning with 1 on row 1, then producing row n by replacing the largest value on row n-1, k, by 1/n and k - 1/n, and arranging the entries in order from smallest to largest.
%C A344007 If there is more than one copy of the largest entry in row n-1, only one copy is changed.
%C A344007 For a somewhat similar triangle, see Leibniz's Harmonic Triangle A003506. - _N. J. A. Sloane_, Jun 09 2021
%e A344007 The triangle's first 10 rows:
%e A344007   1
%e A344007   1/2,   1/2
%e A344007   1/6,   1/3,   1/2
%e A344007   1/6,   1/4,   1/4,   1/3
%e A344007   2/15,  1/6,   1/5,   1/4,   1/4
%e A344007   1/12,  2/15,  1/6,   1/6,   1/5,   1/4
%e A344007   1/12,  3/28,  2/15,  1/7,   1/6,   1/6,   1/5
%e A344007   3/40,  1/12,  3/28,  1/8,   2/15,  1/7,   1/6,   1/6
%e A344007   1/18,  3/40,  1/12,  3/28,  1/9,   1/8,   2/15,  1/7,   1/6
%e A344007   1/18,  1/15,  3/40,  1/12,  1/10,  3/28,  1/9,   1/8,   2/15,  1/7
%e A344007   ...
%e A344007 The denominators are:
%e A344007    1
%e A344007    2,  2,
%e A344007    6,  3, 2,
%e A344007    6,  4, 4, 3,
%e A344007   15,  6, 5, 4, 4,
%e A344007   12, 15, 6, 6, 5, 4,
%e A344007   ...
%o A344007 (PARI) lista(nn) = {my(row, nrow, drow); for (n=1, nn, if (n==1, row = [1], k = vecmax(row); nrow = row; nrow[n-1] = 1/n; nrow = concat(nrow, k - 1/n); row = vecsort(nrow);); drow = apply(denominator, row); for (k=1, #drow, print1(drow[k], ", ")););} \\ _Michel Marcus_, Jun 09 2021
%Y A344007 Cf. A003506.
%Y A344007 For numerators see A344008.
%K A344007 nonn,tabl,frac
%O A344007 1,2
%A A344007 _Evan Lee_, Jun 08 2021