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A203569 Numbers whose digits are a permutation of [0,...,n] and which contain the product of any two adjacent digits as a substring.

%I A203569 #33 Dec 23 2024 14:53:43
%S A203569 0,10,102,120,201,210,1203,1302,2013,2031,2103,2130,3012,3021,3102,
%T A203569 3120,12034,12043,20314,20413,21304,21403,30214,30412,31204,31402,
%U A203569 34012,34120,40213,40312,41203,41302,43012,43120,120345,120543,203145,203154,204153
%N A203569 Numbers whose digits are a permutation of [0,...,n] and which contain the product of any two adjacent digits as a substring.
%C A203569 The subsequence A198298 corresponding to n=9 was suggested by E. Angelini (cf. link).
%C A203569 If we consider permutations of [1,...,n], the only solutions are { 1, 12, 21, 213, 312, 3412, 4312, 71532486 }.
%C A203569 There are 285 terms.
%H A203569 Jason Kimberley, <a href="/A203569/b203569.txt">Table of n, a(n) for n = 1..285</a> (complete sequence)
%H A203569 Eric Angelini, <a href="http://www.cetteadressecomportecinquantesignes.com/DixChiffres.htm">10 different digits, 9 products</a>
%H A203569 E. Angelini, <a href="/A198298/a198298.pdf">10 different digits, 9 products</a> [Cached copy, with permission]
%H A203569 E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2012-January/008824.html">10 different digits, 9 products</a>, Posting to Seqfan List, Jan 03 2012
%e A203569 The term 12034 is in the sequence since 1*2=2, 2*0=0, 0*3=0 and 3*4=12 are all substrings of 12034. This is the least nontrivial term in the sense that it contains two adjacent digits > 1, which is the case for all solutions > 42000.
%o A203569 (PARI) n_digit_terms(n)={ my(a=[],p=vector(n,i,10^(n-i))~,t);for(i=(n-1)!,n!-1, is_A203565(t=numtoperm(n,i)%n*p) & a=concat(a,t));vecsort(a)}
%Y A203569 Cf. A198298, A203566, A210013-A210020.
%K A203569 nonn,base,fini,full
%O A203569 1,2
%A A203569 _M. F. Hasler_, Jan 03 2012