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%I #12 Jul 22 2021 02:09:39
%S 51,59,69,113,124,125,135,136,139,149,150,151,164,165,166,179,180,181,
%T 195,196,199,209,210,211
%N Numbers k such that the minimal mark in a length k sparse ruler is round(sqrt(9 + 12*k)/2) + 1.
%C Other sparse rulers in the range length 1 to 213 have round(sqrt(9 + 12*k)/2) minimal marks.
%C Minimal vertices in k-edge graceful graph = minimal marks in length k sparse ruler.
%C Minimal marks can be derived from A004137 and using zero-count values in A103300.
%C Conjecture: Minimal marks k - round(sqrt(9 + 12*k)/2) is always 0 or 1.
%H P. Luschny, <a href="http://www.luschny.de/math/rulers/rulerpyramid.html">The Perfect Ruler Pyramid (1-101)</a>
%H P. Luschny, <a href="http://www.luschny.de/math/rulers/rulercnt.html">Perfect and Optimal Rulers</a>
%Y Cf. A046693, A004137, A103300, A103294.
%K nonn,hard,more
%O 1,1
%A _Ed Pegg Jr_, Jun 23 2019
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