cp's OEIS Frontend

A283161 Natural numbers whose digits can be formed by typing non-adjacent keys on a 123-456-789 keypad without repeating a digit.

%I A283161 #14 Apr 06 2017 21:24:15
%S A283161 1,2,3,4,5,6,7,8,9,13,15,16,17,18,19,24,26,27,28,29,31,34,35,37,38,39,
%T A283161 42,43,46,48,49,51,53,57,59,61,62,64,67,68,71,72,73,75,76,79,81,82,83,
%U A283161 84,86,91,92,93,94,95,97,135,137,138,139,153,157,159,167,168,173,175,176,179,183,186,193,195
%N A283161 Natural numbers whose digits can be formed by typing non-adjacent keys on a 123-456-789 keypad without repeating a digit.
%C A283161 Or say numbers which are "very difficult" to be typed on a keypad without the zero. (See description of A215009.)
%H A283161 FUNG Cheok Yin, <a href="/A283161/b283161.txt">Table of n, a(n) for n = 1..453</a>
%H A283161 FUNG Cheok Yin, <a href="/A283161/a283161.cpp.txt">C++ program</a>
%e A283161 The keypad is:
%e A283161 +-----+
%e A283161 |1|2|3|
%e A283161 +-+-+-+
%e A283161 |4|5|6|
%e A283161 +-+-+-+
%e A283161 |7|8|9|
%e A283161 +-+-+-+
%e A283161 It is visibly obvious that 168 can be formed on the keypad, and each pairwise digits of 168 are not adjacent.
%t A283161 no = IntegerDigits @ {12,14,23,25,34,36,45,47,56,58,69,78,89}; Sort[ FromDigits /@ Flatten[ Permutations /@ Select[ Subsets[ Range@ 9, {1, 9}], Intersection[ Subsets[#, {2}], no] == {} &], 1]] (* _Giovanni Resta_, Apr 06 2017 *)
%Y A283161 Cf. A280593, A215009, A006506(3)
%K A283161 nonn,fini,full,base
%O A283161 1,2
%A A283161 _FUNG Cheok Yin_, Mar 02 2017