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A152054 Bouncy numbers (numbers whose digits are in neither increasing nor decreasing order). 6

%I

%S 101,102,103,104,105,106,107,108,109,120,121,130,131,132,140,141,142,

%T 143,150,151,152,153,154,160,161,162,163,164,165,170,171,172,173,174,

%U 175,176,180,181,182,183,184,185,186,187,190,191,192,193,194,195,196

%N Bouncy numbers (numbers whose digits are in neither increasing nor decreasing order).

%C Complement of union of A009994 and A009996. - _Ray Chandler_, Oct 25 2011

%C Number of n-digit bouncy numbers is 9*10^(n-1) - (n+18)*binomial(n+8, 8)/9 + 10. - _Altug Alkan_, Oct 02 2018

%H David F. Marrs, <a href="/A152054/b152054.txt">Table of n, a(n) for n = 1..10000</a>

%H Project Euler, <a href="http://projecteuler.net/problem=113">Non-bouncy numbers Problem 113</a>

%t Select[Range[0,200], !LessEqual@@IntegerDigits[#] && !GreaterEqual@@IntegerDigits[#]&] (* _Ray Chandler_, Oct 25 2011 *)

%t bnQ[n_]:=Module[{didn=Differences[IntegerDigits[n]]},Count[didn,_?(#>0&)]>0 && Count[didn,_?(#<0&)]>0]; Select[Range[100,200],bnQ] (* _Harvey P. Dale_, Jun 13 2020 *)

%o (Python)

%o a = 1

%o b = 100

%o while a != 51:

%o if str(b) != ''.join(sorted(str(b))) and str(b) != ''.join(sorted(str(b)))[::-1]:

%o print(b)

%o a += 1

%o b += 1

%o # _David F. Marrs_, Sep 25 2018

%Y Cf. A152464. - _Jon E. Schoenfield_, Dec 06 2008

%Y Cf. A009994, A009996, A204692.

%K nonn,base,easy

%O 1,1

%A Jerome Abela (Jerome.Abela(AT)gmail.com), Nov 22 2008

%E More terms from _Jon E. Schoenfield_, Dec 06 2008

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Last modified July 30 14:56 EDT 2021. Contains 346359 sequences. (Running on oeis4.)