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

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, 54321, 64320, 64321, 65210, 764210

Offset: 1

Author

Christian Perfect, Jul 16 2015

Keywords

• nonn
• base
• fini
• full

Comments

Intersection of A009995 and A023797. - Michel Marcus, Jul 16 2015

Examples

			54321 belongs to the sequence because its digits are strictly decreasing and its hexadecimal representation, D431, also has strictly decreasing digits.
976210 doesn't belong to the sequence because, while its decimal digits are strictly decreasing, its hexadecimal representation EE552 is not strictly decreasing.
		

Links

• Tweet by Wolfram|Alpha Can't

Crossrefs

Cf. A009995 (in base 10 only), A023797 (in base 16 only).

Programs

Mathematica

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 *)

Python

def decreasing(top):
    if top==0:
        yield []
        return
    for d in range(top):
        if d>0:
            yield [d]
        for s in decreasing(d):
            yield [d]+s
def to_int(s):
    t = 0
    for d in s:
        t = t*10+d
    return t
def to_hex(n):
    out = []
    if n==0:
        return [0]
    while n:
        m = n%16
        n = (n-m)//16
        out.insert(0,m)
    return out
def is_decreasing(h):
    m = h[0]
    for d in h[1:]:
        if d>=m:
            return False
        m = d
    return True
ns = sorted(to_int(s) for s in list(decreasing(10)))
a = [n for n in ns if is_decreasing(to_hex(n))]