cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A050278 Pandigital numbers: numbers containing the digits 0-9. Version 1: each digit appears exactly once.

Original entry on oeis.org

1023456789, 1023456798, 1023456879, 1023456897, 1023456978, 1023456987, 1023457689, 1023457698, 1023457869, 1023457896, 1023457968, 1023457986, 1023458679, 1023458697, 1023458769, 1023458796, 1023458967, 1023458976, 1023459678, 1023459687, 1023459768
Offset: 1

Views

Author

Eric W. Weisstein, Dec 11 1999

Keywords

Comments

This is a finite sequence with 9*9! = 3265920 terms: a(9*9!) = 9876543210.
A171102 is the infinite version, where each digit must appear at least once.
More precisely, this is exactly the subset of the first 9*9! terms of A171102. - M. F. Hasler, Jan 05 2020
Subsequence of A134336 and of A178403; A178401(a(n)) = 1. - Reinhard Zumkeller, May 27 2010
Smallest prime factors: A178775(n) = A020639(a(n)). - Reinhard Zumkeller, Jun 11 2010
A178788(a(n)) = 1. - Reinhard Zumkeller, Jun 30 2010
All these numbers are composite because the sum of the digits, 45, is divisible by 9. - T. D. Noe, Nov 09 2011
This is the 10th row of the array T(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. A220076 is the 6th row. A218019 is the 7th row. A219743 is the 8th row. - Jonathan Vos Post, Dec 05 2012
From Hieronymus Fischer, Feb 13 2013: (Start)
The sum of all terms is 9!*49444444440 = 17942399998387200.
General formula for the sum of all terms of the finite sequence of the corresponding base-p pandigital numbers with p places: sum = ((p^2 - p - 1)*(p^p - 1) + p - 1)*(p-2)!/2.
General formula for the sum of all terms (interpreted as decimal permutational numbers with exactly d+1 different digits from the range 0..d < 10): sum = (d+1)!*((10d - 1)*10^d - d + 1)/18, d > 1.
(End)

Links

Crossrefs

Cf. A171102, A050288, A050289.
Cf. A199630, A199631, A114260, A199632, A199633.
Cf. A031969, A050278, A220063, A220076, A218019, A219743.

Programs

  • Mathematica
    Select[ FromDigits@# & /@ Permutations[ Range[0, 9]], # > 10^9 &, 20] (* Robert G. Wilson v, May 30 2010, Jan 17 2012 *)
  • PARI
    A050278(n)={ my(b=vector(9,k,1+(n+9!-1)%(k+1)!\k!), t=b[9]-1, d=vector(9,i,i+(i>t)-1)); for(i=1,8, t=10*t+d[b[9-i]]; d=vecextract(d,Str("^"b[9-i]))); t*10+d[1]} \\ M. F. Hasler, Jan 15 2012
  • PARI
    is_A050278(n)={ 9<#vecsort(Vecsmall(Str(n)),,8) & n<1e10 } /* assuming that n is a nonnegative integer */ /* M. F. Hasler, Jan 10 2012 */
  • PARI
    a(n)=my(d=numtoperm(10,n+9!-1));sum(i=1,#d,(d[i]-1)*10^(#d-i)) \\ David A. Corneth, Jun 01 2014
  • Python
    from itertools import permutations
A050278_list = [int(''.join(d)) for d in permutations('0123456789',10) if d[0] != '0'] # Chai Wah Wu, May 25 2015

Formula

A050278 = 9*A171571. - M. F. Hasler, Jan 12 2012
A050278(n) = A171102(n) for n <= 9*9!.

Extensions

Edited by N. J. A. Sloane, Sep 25 2010 to clarify that this is a finite sequence

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

Views

Author

Jonathan Vos Post, Dec 03 2012

Keywords

Comments

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.

Crossrefs

Cf. A031969, A050278, A220063.

Programs

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

Extensions

Corrected by T. D. Noe, Dec 04 2012

A218019 Integers in which the number of distinct base-10 digits is 7.

Original entry on oeis.org

1023456, 1023457, 1023458, 1023459, 1023465, 1023467, 1023468, 1023469, 1023475, 1023476, 1023478, 1023479, 1023485, 1023486, 1023487, 1023489, 1023495, 1023496, 1023497, 1023498, 1023546, 1023547, 1023548, 1023549, 1023564, 1023567, 1023568, 1023569
Offset: 1

Views

Author

Jonathan Vos Post, Dec 04 2012

Keywords

Comments

This is to A031969 as 7 is to 4. This is the 7th 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. A220076 is the 6th row. Pandigital numbers A050278 is the 10th row. The subsequence of primes begins: 1023467, 1023487.

Crossrefs

Cf. A031969, A050278, A220063, A220076.

Programs

  • Mathematica
    Select[Range[1000000, 1030000], Length[Union[IntegerDigits[#]]] == 7 &] (* T. D. Noe, Dec 04 2012 *)

A277459 Decades with the same semiprime pattern as the next decade.

Original entry on oeis.org

102, 387, 433, 436, 527, 656, 882, 1108, 1181, 1531, 1546, 1555, 1667, 1797, 1822, 1823, 1913, 1991, 2009, 2074, 2083, 2151, 2311, 2353, 2370, 2615, 2626, 2646, 2671, 3202, 3232, 3256, 3278, 3293, 3371, 3413, 3511, 3599, 3634, 3904, 3929, 3934, 4123, 4152
Offset: 1

Views

Author

Bobby Jacobs and N. J. A. Sloane, Oct 16 2016

Keywords

Examples

			a(1)=102 because the decade from 1020 to 1029 has the same semiprime pattern as the decade from 1030 to 1039 (1027 and 1037).

Crossrefs

Cf. A220063, A277460.

Formula

a(n) = A220063(n)-2.
a(n) = A277460(n)-1.

A277460 Decades with the same semiprime pattern as the previous decade.

Original entry on oeis.org

103, 388, 434, 437, 528, 657, 883, 1109, 1182, 1532, 1547, 1556, 1668, 1798, 1823, 1824, 1914, 1992, 2010, 2075, 2084, 2152, 2312, 2354, 2371, 2616, 2627, 2647, 2672, 3203, 3233, 3257, 3279, 3294, 3372, 3414, 3512, 3600, 3635, 3905, 3930, 3935, 4124, 4153
Offset: 1

Views

Author

Bobby Jacobs and N. J. A. Sloane, Oct 16 2016

Keywords

Examples

			a(1)=103 because the decade from 1020 to 1029 has the same semiprime pattern as the decade from 1030 to 1039 (1027 and 1037).

Crossrefs

Cf. A220063, A277459.

Formula

a(n) = A220063(n)-1.
a(n) = A277459(n)+1.

A220343 The number of decades below 10^n whose semiprime pattern is the same as semiprime pattern in the previous decade.

Original entry on oeis.org

0, 0, 7, 114, 1794, 24605
Offset: 1

Views

Author

Robert G. Wilson v, Jonathan Vos Post, Dec 11 2012

Keywords

Examples

			a(3) = 7 because the 7 values less than 10^3 are 104, 389, 435, 438, 529, 658, 884.

Crossrefs

Cf. A220063.
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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