A050278 -id:A050278 - cp's OEIS frontend

A199631 Numbers having each digit once and whose cube has each digit three times.

4680215379, 4752360918, 4765380219, 4915280637, 5063248197, 5164738920, 5382417906, 5426370189, 5429013678, 5628130974, 5679321048, 5697841320, 5762831940, 5783610492, 5786430129, 5903467821, 6019285734, 6053147982, 6095721483, 6143720958, 6158723094

Offset: 1

T. D. Noe, Nov 09 2011

			4680215379^3 = 102517384602327906545167884939.

T. D. Noe, Table of n, a(n) for n = 1..74 (all terms).
Patrick De Geest, The nine digits (page 4) with some ten digit (pandigital) exceptions
Author?, All terms

Cf. A050278 (pandigital numbers), A199630, A365144, A199632, A199633. Subsequence of A114259.

t = Select[Permutations[Range[0, 9]], #[[1]] > 0 &]; t2 = Select[t, Union[DigitCount[FromDigits[#]^3]] == {3} &]; FromDigits /@ t2

A199632 Numbers having each digit once and whose 5th power has each digit five times.

Original entry on oeis.org

7351062489, 8105632794, 8401253976, 8731945026, 9164072385, 9238750614, 9615278340, 9847103256

Offset: 1

T. D. Noe, Nov 09 2011

There are 8 numbers total. Subsequence of A114261.

			7351062489 ^5 = 21465972705539303240727164839587886180361092651449.

Patrick De Geest, The nine digits (page 4) with some ten digit (pandigital) exceptions
Author?, All terms

Cf. A050278 (pandigital numbers), A199630, A199631, A114260, A114261, A199633.

t = Select[Permutations[Range[0, 9]], #[[1]] > 0 &]; t2 = Select[t, Union[DigitCount[FromDigits[#]^5]] == {5} &]; FromDigits /@ t2

A199633 Numbers having each digit once and whose 6th power has each digit six times.

Original entry on oeis.org

7025869314, 7143258096, 7931584062, 8094273561, 8920416357, 9247560381

Offset: 1

T. D. Noe, Nov 09 2011

There are 6 numbers total. There are no higher powers with this property.

			7025869314 ^6 = 120281934463386157260042215510596389732740014997586987548736.

Patrick De Geest, The nine digits (page 4) with some ten digit (pandigital) exceptions
Author?, All terms

Cf. A050278 (pandigital numbers), A199630, A199631, A365144, A199632.

t = Select[Permutations[Range[0, 9]], #[[1]] > 0 &]; t2 = Select[t, Union[DigitCount[FromDigits[#]^6]] == {6} &]; FromDigits /@ t2

A134336 Nonnegative integers n containing each digit between n's smallest and largest decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88, 89, 98, 99, 100, 101, 102, 110, 111, 112, 120, 121, 122, 123, 132, 201, 210, 211, 212, 213, 221, 222, 223, 231, 232, 233, 234, 243, 312, 321, 322, 323

Offset: 1

Rick L. Shepherd, Oct 21 2007

A032981 is a subsequence; the term 102 is the first positive integer not also in A032981. A171102 (pandigital numbers) and A033075 are subsequences. Union of A010785 (repdigits) and A108965.
a(n) = A178403(n) for n < 48. - Reinhard Zumkeller, May 27 2010
Equivalently, numbers with the property that the set of its decimal digits is a set of consecutive numbers. - Tanya Khovanova and Charles R Greathouse IV, Jul 31 2012

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A032981, A050278, A033075 (a subsequence), A010785, A108965.

is(n)=my(v=vecsort(eval(Vec(Str(n))),,8));for(i=2,#v,if(v[i]!=1+v[i-1],return(0)));1 \\ Tanya Khovanova and Charles R Greathouse IV, Jul 31 2012

is_A134336(n)={vecmax(n=Set(digits(n)))-vecmin(n)==#n-1} \\ M. F. Hasler, Dec 24 2014

def ok(n): d = sorted(set(map(int, str(n)))); return d[-1]-d[0]+1 == len(d)
print([k for k in range(324) if ok(k)]) # Michael S. Branicky, Dec 12 2023

a(n) ~ n. - Charles R Greathouse IV, Sep 09 2011

Edited by N. J. A. Sloane, Aug 06 2012

A365144 Numbers having each digit once and whose 4th power has each digit four times.

Original entry on oeis.org

5702631489, 7264103985, 7602314895, 7824061395, 8105793624, 8174035962, 8304269175, 8904623175, 8923670541, 9451360827, 9785261403, 9804753612, 9846032571

Offset: 1

T. D. Noe, Nov 09 2011

Currently same terms as A114260, but that sequence has more terms to follow. - Ray Chandler, Aug 23 2023

			5702631489 is a term since its 4th power 1057550783692741389295697108242363408641 contains four 5's, four 7's, four 0's and so on.

Cf. A050278 (pandigital numbers), A199630, A199631, A199633. Subsequence of A114260.

t = Select[Permutations[Range[0, 9]], #[[1]] > 0 &]; t2 = Select[t, Union[DigitCount[FromDigits[#]^4]] == {4} &]; FromDigits /@ t2 (* T. D. Noe, Nov 08 2011 *)

A178401 Number of times the rounded up arithmetic mean of digits of n occurs in n, cf. A004427.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 0, 0

Offset: 0

Reinhard Zumkeller, May 27 2010

a(A178402(n)) = 0; a(A050278(n)) = 1; a(A178403(n)) > 0;

a(A010785(n)) > 0; a(A178358(n)) > 0; a(A178359(n)) > 0.

R. Zumkeller, Table of n, a(n) for n = 0..25000

A115922 Numbers k such that k and 2*k, taken together are pandigital.

Original entry on oeis.org

13485, 13548, 13845, 14538, 14685, 14835, 14853, 14865, 15486, 16485, 18546, 18645, 20679, 20769, 20793, 23079, 26709, 26907, 27069, 27093, 27309, 29067, 29073, 29307, 30729, 30792, 30927, 31485, 32079, 32709, 32907, 34851, 35148, 35481, 38145, 38451

Offset: 1

Giovanni Resta, Feb 06 2006

Sequence contains 48 terms, the largest being 48651.

If leading zeros are permitted, there are 12 additional terms: 6729, 6792, 6927, 7269, 7293, 7329, 7692, 7923, 7932, 9267, 9273, 9327. - Harvey P. Dale, Feb 09 2014

			13485 and 26970=13485*2 together contain all the 10 digits once.

Nathaniel Johnston, Table of n, a(n) for n = 1..48 (full sequence)

Cf. A050278, A054383, A115923, A115924, A115925, A114126, A115927.

for n from 12345 to 49382 do d:=[op(convert(n,base,10)), op(convert(2*n,base,10))]: pandig:=true: for k from 0 to 9 do if(numboccur(k,d)<>1)then pandig:=false: break: fi: od: if(pandig)then print(n): fi: od: # Nathaniel Johnston, May 31 2011

onehalfQ[n_]:=FromDigits[Take[n,5]]/FromDigits[Take[n,-5]]==1/2; FromDigits[ Take[#,5]]&/@Select[Permutations[Range[0,9]],onehalfQ] (* This program generates the full 60-term sequence, with leading zeros permitted, of which this sequence is a subset -- see Comments *) (* Harvey P. Dale, Feb 09 2014 *)

{for(n=10234,49876,#Set(digits(n))==5||next; #Set(digits(n*2))==5 && #Set(concat(digits(n),digits(n*2)))==10 && print1(n","))} \\ M. F. Hasler, Feb 08 2014

A180489 Smallest pandigital number (A171102) divisible by the n-th prime A000040(n).

Original entry on oeis.org

1023456798, 1023456789, 1023467895, 1023456798, 1024375869, 1023456798, 1023457698, 1023458769, 1023475689, 1023468957, 1023458769, 1023654987, 1023458769, 1023469875, 1023467958, 1023459786, 1023457896, 1023458976

Offset: 1

Lekraj Beedassy, Sep 08 2010

Digits may appear more than once in the multiple, resulting in 11-or-more-digit values of a(n). The first entry for which that happens is a(10545), because the smallest multiple of the 10545th prime 111119 that contains all the digits 0-9 is 92373 * 111119 = 10264395387, and all smaller primes have 10-digit pandigital multiples. - David J. Seal, Sep 18 2017

			a(1) is the smallest pandigital number divisible by prime(1) = 2, which is 1023456798. - _David J. Seal_, Sep 18 2017

Ray Chandler, Table of n, a(n) for n=1..10000

Cf. A050278, A061604, A171102, A274328.

With[{s = Select[FromDigits@ # & /@ Permutations[Range[0, 9], {10}], # > 10^9 &]}, Table[SelectFirst[s, Divisible[#, Prime@ n] &], {n, 18}]] (* Michael De Vlieger, Sep 18 2017, after Robert G. Wilson v at A171102 *)

A220076 Numbers with exactly six distinct base-10 digits.

Original entry on oeis.org

102345, 102346, 102347, 102348, 102349, 102354, 102356, 102357, 102358, 102359, 102364, 102365, 102367, 102368, 102369, 102374, 102375, 102376, 102378, 102379, 102384, 102385, 102386, 102387, 102389, 102394, 102395, 102396, 102397, 102398, 102435, 102436

Offset: 1

Jonathan Vos Post, Dec 03 2012

This is to A031969 as 6 is to 4. This is the 6th row of the array A(k,n) = n-th number in which the number of distinct base-10 digits is k. A031969 is the 4th row. A220063 is the 5th row. Pandigital numbers A050278 is the 10th row. The subsequence of primes begins: 102359, 102367, 102397, 102437.

Cf. A031969, A050278, A220063.

Select[Range[100000, 103000], Length[Union[IntegerDigits[#]]] == 6 &] (* T. D. Noe, Dec 04 2012 *)

Corrected by T. D. Noe, Dec 04 2012

A067898 Least digit not used in n (or 10 if n is pandigital).

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 2, 2

Offset: 0

Rick L. Shepherd, May 13 2003

a(A050278(1)) = a(1023456789) = 10, the first term with that value, as 1023456789 is the first base 10 pandigital number.

a(A052382(n)) = 0; a(A011540(n)) > 0. [Reinhard Zumkeller, May 04 2012]

			a(10)=2 because decimal digits 0 and 1 are both used in 10, a(102)=3 because decimal digits 0, 1 and 2 are used in 102.

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A050278 (pandigital numbers).

Cf. A212193 (ternary).

import Data.List (delete)
a067898 n = f n [0..10] where
   f x ys | x <= 9    = head $ delete x ys
          | otherwise = f x' $ delete d ys where (x',d) = divMod x 10
-- Reinhard Zumkeller, May 04 2012

def A067898(n):
    s = set(str(n))
    for i in range(10):
        if str(i) not in s:
            return i
    return 10 # Chai Wah Wu, Apr 13 2024

cp's OEIS Frontend

A199631 Numbers having each digit once and whose cube has each digit three times.

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A199632 Numbers having each digit once and whose 5th power has each digit five times.

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Mathematica

A199633 Numbers having each digit once and whose 6th power has each digit six times.

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Mathematica

A134336 Nonnegative integers n containing each digit between n's smallest and largest decimal digits.

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A365144 Numbers having each digit once and whose 4th power has each digit four times.

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A178401 Number of times the rounded up arithmetic mean of digits of n occurs in n, cf. A004427.

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A115922 Numbers k such that k and 2*k, taken together are pandigital.

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A180489 Smallest pandigital number (A171102) divisible by the n-th prime A000040(n).

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