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

1,1

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

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 *)

Prog

(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

Crossrefs

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

Cf. A009994, A009996, A204692.

Sequence in context: A284180 A138719 A043639 * A296883 A183086 A134808

Adjacent sequences: A152051 A152052 A152053 * A152055 A152056 A152057

Keyword

nonn,base,easy

Author

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

Extensions

More terms from Jon E. Schoenfield, Dec 06 2008

Status

approved