A204692 -id:A204692 - cp's OEIS frontend

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

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

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

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

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

Cf. A009994, A009996, A204692.

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 *)

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

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

More terms from Jon E. Schoenfield, Dec 06 2008

A364342 a(n) is the number of base-10 nonbouncy numbers below 10^n.

Original entry on oeis.org

10, 100, 475, 1675, 4954, 12952, 30817, 67987, 140907, 277033, 520565, 940455, 1641355, 2778305, 4576113, 7354549, 11560664, 17809754, 26936719, 40059819, 58659104, 84672094, 120609609, 169694999, 236030401, 324794055, 442473145, 597137095, 798756745, 1059575359

Offset: 1

Peter Cullen Burbery, Jul 19 2023

A bouncy number has digits that are neither monotonically increasing nor decreasing from left to right. A nonbouncy number is a number that is not bouncy. That is, either the digits are monotonically increasing or they are monotonically decreasing from left to right.

			a(3) = 475 because binomial(3+9, 3) + (3+1)*binomial(3+10, 3+1)/10 - 10*3 - 1 = 475.
a(4) = 1675 because binomial(4+9, 4) + (4+1)*binomial(4+10, 4+1)/10 - 10*4 - 1 = 1675.

Project Euler, Problem 113. Non-bouncy numbers.
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A152054, A204692.

a[n_] := -1 - 10 n + Binomial[9 + n, n] + 1/10 (1 + n) Binomial[10 + n, 1 + n]; Table[a[n], {n, 100}]

a(1) = 10, a(2) = 100. For n > 2, a(n) = binomial(n+9, n) + (n+1)*binomial(n+10, n+1)/10 - 10*n - 1.

G.f.: x*(10 - 10*x - 75*x^2 + 300*x^3 - 546*x^4 + 588*x^5 - 390*x^6 + 150*x^7 - 25*x^8 - 2*x^9 + x^10)/(1 - x)^11. - Stefano Spezia, Jul 20 2023

cp's OEIS Frontend

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

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