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

101, 102, 103, 104, 105, 106, 107, 108, 109, 120, 121, 130, 131, 132, 140, 141, 142, 143, 150, 151, 152, 153, 154, 160, 161, 162, 163, 164, 165, 170, 171, 172, 173, 174, 175, 176, 180, 181, 182, 183, 184, 185, 186, 187, 190, 191, 192, 193, 194, 195, 196

Offset: 1

Author

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

Keywords

• nonn
• base
• easy

Comments

Complement of union of A009994 and A009996. - Ray Chandler, Oct 25 2011

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

Links

• David F. Marrs, Table of n, a(n) for n = 1..10000
• Project Euler, Non-bouncy numbers Problem 113

Crossrefs

Cf. A152464. - Jon E. Schoenfield, Dec 06 2008

Cf. A009994, A009996, A204692.

Programs

Mathematica

Select[Range[0,200], !LessEqual@@IntegerDigits[#] && !GreaterEqual@@IntegerDigits[#]&] (* Ray Chandler, Oct 25 2011 *)
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 *)

Python

a = 1
b = 100
while a != 51:
    if str(b) != ''.join(sorted(str(b))) and str(b) != ''.join(sorted(str(b)))[::-1]:
        print(b)
        a += 1
    b += 1
# David F. Marrs, Sep 25 2018

Python

from itertools import count, islice
def A152054_gen(startvalue=1): # generator of terms >= startvalue
    for n in count(max(startvalue,1)):
        l = len(s:=tuple(int(d) for d in str(n)))
        for i in range(1,l-1):
            if (s[i-1]-s[i])*(s[i]-s[i+1]) < 0:
                yield n
                break
A152054_list = list(islice(A152054_gen(),30)) # Chai Wah Wu, Jul 28 2023

Extensions

More terms from Jon E. Schoenfield, Dec 06 2008