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%I #13 Jan 02 2023 12:30:50
%S 10,7,0,49,0,28,63,0,14,56,42,21,0,7,28,35,42,28,14,14,7,0,49,14,56,
%T 21,35,28,14,14,56,7,28,7,28,49,0,28,63,7,28,35,42,14,7,21,35,14,56,7,
%U 28,7,28,35,42,49,14,56,49,14,56,28,63,0,14,56,42,21,49,14,56,21,35
%N Start with a(0)=10, then a(n) = 7 times the n-th digit of the sequence.
%C This sequence was inspired by E. Angelini's post to the SeqFan list, cf. links.
%C a(0)=10 is the smallest possible choice to ensure that the digit 0 appears anywhere in the sequence. a(0)=1 would lead to the same sequence with the terms 0 removed.
%C By construction, all terms a(n), n>0, are divisible by 7, and a(n)/7 yields the sequence of digits of the (concatenated) terms of this sequence.
%C It is easy to show that the distance between two 0's is strictly increasing from one occurrence to the next one. Thus, the asymptotic density of terms and/or digits 0 is zero, and the sequence can never "enter a loop".
%H E. Angelini, <a href="http://list.seqfan.eu/oldermail/seqfan/2014-October/013722.html">Brute force density: triples and cubes</a>, SeqFan list, Oct 01 2014
%o (PARI) a(n,s=10,m=7,d=[])={for(i=1,n,print1(s",");d=concat(d,if(s,digits(s)));s=m*d[1];d=vecextract(d,"^1"));s}
%o (Python)
%o def aupton(nn):
%o alst, astr = [10], "X10"
%o for n in range(1, nn+1):
%o alst.append(7 * int(astr[n]))
%o astr += str(alst[-1])
%o return alst
%o print(aupton(72)) # _Michael S. Branicky_, Oct 07 2021
%Y Cf. A248128, A248129, A248130, A248131.
%K nonn,base
%O 0,1
%A _M. F. Hasler_, Oct 02 2014
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