A009995 -id:A009995 - cp's OEIS frontend

A119260 Numbers with even decimal digits in increasing order.

0, 2, 4, 6, 8, 24, 26, 28, 46, 48, 68, 246, 248, 268, 468, 2468

Offset: 1

Zak Seidov, May 11 2006

This is the complete list of all 16 such numbers. Cf. A119261 Even decimal digits in decreasing order, A119253 Odd digits in increasing order, A119252 Odd digits in decreasing order, A009993 Digits in increasing order, A009995 Digits in decreasing order.

Cf. A009993, A009995, A119252, A119253, A119261.

Flatten@Table[FromDigits/@Subsets[Range[2,8,2],{n}],{n,0,5}]

A119261 Numbers with even decimal digits in decreasing order.

Original entry on oeis.org

0, 2, 4, 6, 8, 20, 40, 42, 60, 62, 64, 80, 82, 84, 86, 420, 620, 640, 642, 820, 840, 842, 860, 862, 864, 6420, 8420, 8620, 8640, 8642, 86420

Offset: 1

Zak Seidov, May 11 2006

This is the complete list of all 31 such numbers. Cf. A119260 Even decimal digits in increasing order, A119253 Odd digits in increasing order, A119252 Odd digits in decreasing order, A009993 Digits in increasing order, A009995 Digits in decreasing order.

Cf. A009993, A009995, A119252, A119253, A119260.

Sort@Flatten@Table[FromDigits/@Subsets[Range[8,0,-2],{n}],{n,5}]

A212372 Nonprime numbers with distinct digits in descending order.

Original entry on oeis.org

1, 4, 6, 8, 9, 10, 20, 21, 30, 32, 40, 42, 50, 51, 52, 54, 60, 62, 63, 64, 65, 70, 72, 74, 75, 76, 80, 81, 82, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 98, 210, 310, 320, 321, 410, 420, 430, 432, 510, 520, 530, 531, 532, 540, 542, 543, 610, 620, 621, 630

Offset: 1

Jaroslav Krizek, May 10 2012

Sequence is finite with 935 terms, last term is a(935) = 9876543210.

Complement of A052014 with respect to A009995.

Jaroslav Krizek, Table of n, a(n) for n = 1..935 (complete list).

Cf. A052014 (primes with distinct digits in descending order), A009995 (numbers with distinct digits in descending order).

A178788(a(n)) = 1.

A330350 Table of strictly decreasing sequences with terms in {0, ..., 9}, sorted by length, then lexicographically.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 2, 0, 2, 1, 3, 0, 3, 1, 3, 2, 4, 0, 4, 1, 4, 2, 4, 3, 5, 0, 5, 1, 5, 2, 5, 3, 5, 4, 6, 0, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 7, 0, 7, 1, 7, 2, 7, 3, 7, 4, 7, 5, 7, 6, 8, 0, 8, 1, 8, 2, 8, 3, 8, 4, 8, 5, 8, 6, 8, 7, 9, 0, 9, 1, 9, 2, 9, 3, 9, 4, 9, 5, 9, 6, 9, 7, 9, 8

Offset: 1

M. F. Hasler, Dec 11 2019

Row n lists the digits of A009995(n), just as row n < 1024 of A272011 lists the digits of A262557(n).

			The first rows start
   n | row n
   1 | 0,
   2 | 1,
    ...
  10 | 9,
  11 | 1, 0,
  12 | 2, 0,
  13 | 2, 1,
  14 | 3, 0,
  15 | 3, 1,
  16 | 3, 2,
  17 | 4, 0,
    ...
The Sury paper lists the first rows of length 3, row 56 = (2, 1, 0), row 57 = (3, 1, 0), row 58 = (3, 2, 0), row 59 = (3, 2, 1), row 60 = (4, 1, 0), ...

M. F. Hasler, Table of n, a(n) for n = 1..5120 (rows 1 .. 1023, flattened).
B. Sury, Macaulay Expansion, Amer. Math. Monthly 121 (2014), no. 4, 359--360. MR3183022.

Cf. A009995, A272011, A262557.

concat(0,[digits(n)|n<-[1..99],is_A009995(n)])

A385516 Perfect powers whose digits are in strictly decreasing order.

Original entry on oeis.org

1, 4, 8, 9, 32, 64, 81, 841, 961

Offset: 1

Stefano Spezia, Jul 01 2025

Cf. A001597, A009995, A355060, A355062, A355063, A385517.

perfectPowerQ[n_] := n==1 || GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) Select[Range[1000], perfectPowerQ[#] && Max[Differences[IntegerDigits[#]]]<0 &]

A385517 Perfect powers whose digits are in nonincreasing order.

Original entry on oeis.org

1, 4, 8, 9, 32, 64, 81, 100, 400, 441, 841, 900, 961, 1000, 6400, 7744, 7776, 8000, 8100, 10000, 40000, 44100, 64000, 84100, 90000, 96100, 100000, 640000, 774400, 810000, 1000000, 3200000, 4000000, 4410000, 8000000, 8410000, 8874441, 9000000, 9610000, 9853321, 10000000

Offset: 1

Stefano Spezia, Jul 01 2025

Cf. A001597, A009995, A355060, A355062, A355063, A385516.

perfectPowerQ[n_] :=n==1 || GCD @@ FactorInteger[n][[All, 2]] > 1; (* A001597 *) Select[Range[10^6], perfectPowerQ[#] && Max[Differences[IntegerDigits[#]]]<1 &]

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

Original entry on oeis.org

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

Christian Perfect, Jul 16 2015

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

			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.

Tweet by Wolfram|Alpha Can't

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

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 *)

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))]

A381645 a(n) is the largest integer with distinct digits whose digital sum is n.

Original entry on oeis.org

0, 10, 20, 210, 310, 410, 3210, 4210, 5210, 6210, 43210, 53210, 63210, 73210, 83210, 543210, 643210, 743210, 843210, 943210, 953210, 6543210, 7543210, 8543210, 9543210, 9643210, 9743210, 9843210, 76543210, 86543210, 96543210, 97543210, 98543210, 98643210, 98743210, 98753210, 876543210, 976543210, 986543210, 987543210, 987643210, 987653210, 987654210, 987654310, 987654320, 9876543210

Offset: 0

Gonzalo Martínez, Mar 03 2025

Since all the terms in this list have distinct digits, the highest possible digit sum is that of the number 987654321, which is 45. Therefore, this list is finite and has 46 terms.
All terms == 0 (mod 10).
All terms are members of A009995.

			For n = 5, the integers with distinct digits whose digital sum is 5 are: 5, 14, 23, 32, 41, 50, 104, 140, 203, 230, 302, 320, 401 and 410, where the largest of them is 410. So, a(5) = 410.

Cf. A007953, A009995, A227378.

cp's OEIS Frontend

A119260 Numbers with even decimal digits in increasing order.

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A119261 Numbers with even decimal digits in decreasing order.

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A212372 Nonprime numbers with distinct digits in descending order.

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Formula

A330350 Table of strictly decreasing sequences with terms in {0, ..., 9}, sorted by length, then lexicographically.

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PARI

A385516 Perfect powers whose digits are in strictly decreasing order.

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A385517 Perfect powers whose digits are in nonincreasing order.

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

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Python

A381645 a(n) is the largest integer with distinct digits whose digital sum is n.

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