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.

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A171102 Pandigital numbers: numbers containing the digits 0-9. Version 2: each digit appears at least once.

Original entry on oeis.org

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

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Author

N. J. A. Sloane, Sep 25 2010

Keywords

Comments

This is the infinite version. See A050278 for the finite version.
The first 9*9!=3265920 terms of this sequence are permutations of the digits 0-9 with a(9*9!)=9876543210 (see Version 1, A050278). - Jeremy Gardiner, May 29 2010
Subsequence of A134336 and of A178403; A178401(a(n))>0. - Reinhard Zumkeller, May 27 2010
Smallest prime factors: A178775(n) = A020639(a(n)). - Reinhard Zumkeller, Jun 11 2010
A178788(a(n)) = 1, for n <= 9*9!, else A178788(a(n)) = 0. - Reinhard Zumkeller, Jun 30 2010 [corrected by Hieronymus Fischer, Feb 02 2013]
A230959(a(n)) = 0. - Reinhard Zumkeller, Nov 02 2013
The first term of the sequence absent in A050278 is a(3265921) = 10123456789. Also, the first prime is a(3306373) = 10123457689 = A050288(1). - Zak Seidov, Sep 23 2015
Almost all numbers are in this sequence, in the sense that it has asymptotic density equal to 1. Indeed, the fraction of n-digit numbers which don't have a given digit d is roughly 0.9^n (not exactly because the first digit is chosen among {1..9}) which tends to zero as n -> oo. - M. F. Hasler, Jan 05 2020

Links

Crossrefs

Cf. A050278, A050288, A050289.
Cf. A051264, A051018, A051019, A051020.
Subsequence of A253172.

Programs

  • Mathematica
    Take[ Select[ FromDigits@# & /@ Permutations[ Range[0, 9], {10}], # > 10^9 &], 20] (* Robert G. Wilson v, May 30 2010 *)
  • PARI
    is_A171102(n)=9<#vecsort(Vecsmall(Str(n)),,8) /* assuming that n is a nonnegative integer. In PARI/GP V.2.4 - 2.9 this is faster than other possibilities involving Set(),Vec(),eval() or digits() */ \\ M. F. Hasler, Jan 10 2012, Sep 19 2017
  • PARI
    A171102=A050278 /*** valid for n <= 9*9! ***/ \\ M. F. Hasler, Jan 10 2012

Formula

a(n) = 1011111111 + A178478(n) for n = 1,...,8!. - M. F. Hasler, Jan 10 2012
A171102(n) = A050278(n) for n <= 9*9!.

A253173 Values n, where n = p * q, and n, p, and q together contain all 10 digits at least once, and no digit is in more than one of n, p or q.

Original entry on oeis.org

15628, 15678, 16038, 17082, 17820, 19084, 20457, 20754, 21658, 24507, 26910, 27504, 28156, 28651, 30976, 32890, 34902, 35046, 35496, 36508, 36970, 37096, 37690, 38870, 40596, 40898, 43076, 43670, 45068, 46740, 46970, 47690, 48504, 48592, 50076, 50346
Offset: 1

Views

Author

Randy L. Ekl, Dec 28 2014

Keywords

Examples

			a(1) is 15628 = 4 * 3907, using all 10 digits.
20748 = 13 * 1596, using all 10 digits, but is NOT a member of this sequence, because the digit 1 appears in both p and q.

Crossrefs

Cf. A195814 (a finite subsequence).
Cf. A253172 (a supersequence, which allows for duplicate digits in n, p and q).

Programs

  • PARI
    isok(n) = {fordiv(n, d, q = n/d; sn = vecsort(digits(n),,8); sd = vecsort(digits(d),,8); sq = vecsort(digits(q),,8); sa = vecsort(concat(sn, concat(sd, sq)),,8); if ((#sa == 10) && (#sn + #sd + #sq == 10), return (1));); return (0);} \\ Michel Marcus, Feb 07 2015
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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