V. Bronstein and A. S. Fraenkel, <a href="httphttps://www.jstor.org/stable/2975323">On a curious property of counting sequences</a>, Amer. Math. Monthly, 101 (1994), 560-563.

editing

approved

P:=proc(q, h) local a, b, c, j, k, n; a:=h; print(a);

for n from 1 to q do a:=convert(a, base, 10); b:=0;

for k from 0 to 9 do c:=0; for j from 1 to nops(a) do

if a[j]=k then c:=c+1; fi; od;

if c>0 then b:=b*10^(ilog10(c*10+k)+1)+c*10+k; fi; od;

a:=b; print(a); od; end: P(10, 1); # Paolo P. Lava, Mar 21 2018

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editing

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1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213, 31121314, 41122314, 31221324, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314, 21322314

approved

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proposed

approved

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proposed

Trevor Scheopner, <a href="https://web.archive.org/web/20171109082421/http://pumj.org/docs/Issue1/Article_4.pdf">The Cyclic Nature (and Other Intriguing Properties) of Descriptive Numbers</a>, Princeton Undergraduate Mathematics Journal, Issue 1, Article 4. [Broken link?]

Madras Math's Amazing Number Facts, <a href="https://web.archive.org/web/20041105013844/http://www.users.zetnet.co.uk/madras/maths/amazingnofacts/fact013.html">Fact No. 13</a>

Madras Math, <a href="https://web.archive.org/web/20041103085145/http://www.users.zetnet.co.uk/madras/maths/descriptive6.html">Descriptive Number</a>

Trevor Scheopner, <a href="http://pumj.org/docs/Issue1/Article_4.pdf">The Cyclic Nature (and Other Intriguing Properties) of Descriptive Numbers</a>, Princeton Undergraduate Mathematics Journal, Issue 1, Article 4. [Broken link?]

proposed

editing