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A260096 Numbers whose decimal and hexadecimal representations both have strictly decreasing digits.

%I A260096 #18 May 23 2020 13:14:03
%S A260096 0,1,2,3,4,5,6,7,8,9,10,32,50,64,65,80,81,82,83,84,96,97,98,210,54320,
%T A260096 54321,64320,64321,65210,764210
%N A260096 Numbers whose decimal and hexadecimal representations both have strictly decreasing digits.
%C A260096 Intersection of A009995 and A023797. - _Michel Marcus_, Jul 16 2015
%H A260096 <a href="https://twitter.com/wacnt/status/621469453138538496">Tweet by Wolfram|Alpha Can't</a>
%e A260096 54321 belongs to the sequence because its digits are strictly decreasing and its hexadecimal representation, D431, also has strictly decreasing digits.
%e A260096 976210 doesn't belong to the sequence because, while its decimal digits are strictly decreasing, its hexadecimal representation EE552 is not strictly decreasing.
%t A260096 dec[v_] := 0 > Max@ Differences@ v; Select[ Union[ FromDigits/@ Select[ Flatten[ Permutations/@ Subsets[ Range[0, 9]], 1], dec]], dec@ IntegerDigits[#, 16] &] (* _Giovanni Resta_, Jul 16 2015 *)
%o A260096 (Python)
%o A260096 def decreasing(top):
%o A260096     if top==0:
%o A260096         yield []
%o A260096         return
%o A260096     for d in range(top):
%o A260096         if d>0:
%o A260096             yield [d]
%o A260096         for s in decreasing(d):
%o A260096             yield [d]+s
%o A260096 def to_int(s):
%o A260096     t = 0
%o A260096     for d in s:
%o A260096         t = t*10+d
%o A260096     return t
%o A260096 def to_hex(n):
%o A260096     out = []
%o A260096     if n==0:
%o A260096         return [0]
%o A260096     while n:
%o A260096         m = n%16
%o A260096         n = (n-m)//16
%o A260096         out.insert(0,m)
%o A260096     return out
%o A260096 def is_decreasing(h):
%o A260096     m = h[0]
%o A260096     for d in h[1:]:
%o A260096         if d>=m:
%o A260096             return False
%o A260096         m = d
%o A260096     return True
%o A260096 ns = sorted(to_int(s) for s in list(decreasing(10)))
%o A260096 a = [n for n in ns if is_decreasing(to_hex(n))]
%Y A260096 Cf. A009995 (in base 10 only), A023797 (in base 16 only).
%K A260096 nonn,base,fini,full
%O A260096 1,3
%A A260096 _Christian Perfect_, Jul 16 2015