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

1,3

Comments

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

Links

Table of n, a(n) for n=1..30.

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Example

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.

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 *)

Prog

(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))]

Crossrefs

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

Sequence in context: A161978 A132579 A004850 * A141709 A330192 A062683

Adjacent sequences: A260093 A260094 A260095 * A260097 A260098 A260099

Keyword

nonn,base,fini,full

Author

Christian Perfect, Jul 16 2015

Status

approved