cp's OEIS Frontend

A248153 Start with a(0)=10, then a(n) = 7 times the n-th digit of the sequence.

%I A248153 #14 Dec 23 2024 14:53:44
%S A248153 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 A248153 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 A248153 28,7,28,35,42,49,14,56,49,14,56,28,63,0,14,56,42,21,49,14,56,21,35
%N A248153 Start with a(0)=10, then a(n) = 7 times the n-th digit of the sequence.
%C A248153 This sequence was inspired by E. Angelini's post to the SeqFan list, cf. links.
%C A248153 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 A248153 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 A248153 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 A248153 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2014-October/013722.html">Brute force density: triples and cubes</a>, SeqFan list, Oct 01 2014
%o A248153 (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 A248153 (Python)
%o A248153 def aupton(nn):
%o A248153     alst, astr = [10], "X10"
%o A248153     for n in range(1, nn+1):
%o A248153         alst.append(7 * int(astr[n]))
%o A248153         astr += str(alst[-1])
%o A248153     return alst
%o A248153 print(aupton(72)) # _Michael S. Branicky_, Oct 07 2021
%Y A248153 Cf. A248128, A248129, A248130, A248131.
%K A248153 nonn,base
%O A248153 0,1
%A A248153 _M. F. Hasler_, Oct 02 2014