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%I #22 Dec 17 2020 12:34:28
%S 1633956,1633965,1659336,1659933,1693365,1775428,1775442,1778425,
%T 1783365,1853394,1853397,1923956,1923965,1932956,1932965,1936690,
%U 1936940,1936970,1942593,1942598,1952493,1952498,1963940,1963970,1966390,1986532,2335689,2336593,2336598,2339563,2339956,2339965
%N Integers N that yield exactly 10 different digits when all products of two successive digits of N are considered.
%C nDigits Count Min Max
%C ------- ----- ---------- ----------
%C 6 0
%C 7 286 1633956 9985197
%C 8 1254 11561774 99851332
%C 9 1708 113245177 985113324
%C 10 468 1123315817 9185132117
%C 11 0
%C There are no 6-digit or 11-digit integers that produce the digits 0 to 9 by multiplication of two contiguous digits of N. The smallest such integer is 1633956; the largest one is 9185132117; the sequence has 3716 terms.
%H Lars Blomberg, <a href="/A296450/b296450.txt">Table of n, a(n) for n = 1..3716</a>
%e The first term is 1633956. The successive products of two contiguous digits of 1633956 are 1*6=6, 6*3=18, 3*3=9, 3*9=27, 9*5=45, 5*6=30. We see that 6, 18, 9, 27, 45 and 30 include all digits 0 to 9, none being repeated.
%t Select[Range[163*10^4,234*10^4],Sort[Flatten[IntegerDigits/@ (Times@@@ Partition[ IntegerDigits[ #],2,1])]]==Range[0,9]&] (* _Harvey P. Dale_, Dec 17 2020 *)
%K nonn,base,fini
%O 1,1
%A _Eric Angelini_ and _Lars Blomberg_, Dec 13 2017
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