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 1-3 of 3 results.

A191820 A178478(n)/9.

Original entry on oeis.org

1371742, 1371743, 1371752, 1371754, 1371763, 1371764, 1371842, 1371843, 1371862, 1371865, 1371873, 1371875, 1371952, 1371954, 1371962, 1371965, 1371984, 1371985, 1372063, 1372064, 1372073, 1372075, 1372084, 1372085, 1372742, 1372743, 1372752
Offset: 1

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Author

Nathaniel Johnston, Jun 24 2011

Keywords

Comments

There are 8!=40320 terms in this finite sequence. Its origin is the fact that numbers whose decimal expansion is a permutation of 12345678 are all divisible by 9.

Links

Crossrefs

Cf. A178485, A178486, A191819.

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!.

A209280 First difference of A050289 = numbers whose digits are a permutation of (1,...,9).

Original entry on oeis.org

9, 81, 18, 81, 9, 702, 9, 171, 27, 72, 18, 693, 18, 72, 27, 171, 9, 702, 9, 81, 18, 81, 9, 5913, 9, 81, 18, 81, 9, 1602, 9, 261, 36, 63, 27, 594, 18, 162, 36, 162, 18, 603, 9, 171, 27, 72, 18, 5814, 9, 171, 27, 72, 18, 603, 9, 261, 36, 63, 27, 1584, 27, 63, 36, 261, 9
Offset: 1

Views

Author

M. F. Hasler, Jan 12 2013

Keywords

Comments

This sequence is the natural extension of A107346 (and others, see below) from 5!-1 to 9!-1 terms, which is the natural (since maximal) length, given that OEIS sequence data are stored as decimal numbers. On the other hand, it is quite different from A219664 in many aspects, not only for the reason that the other sequence is infinite and therefore differs from this one in all terms beyond n = 9!-1.
The sequence is finite, with 9!-1 terms, and symmetric: a(n)=a(9!-n).
All terms are multiples of 9, cf. formula.
The subsequence of the first n!-1 terms (n=2,...,9) yields the first differences of the sequence of numbers whose digits are a permutation of (1,...,n):
The first 8!-1 terms yield the first differences of A178478: numbers whose digits are a permutation of 12345678.
The first 7!-1 terms yield the first differences of A178477: numbers whose digits are a permutation of 1234567.
The first 6!-1 terms yield the first differences of A178476: numbers whose digits are a permutation of 123456.
The first 5!-1 terms yield A107346, the first differences of A178475: numbers whose digits are a permutation of 12345.

Examples

			The same initial terms are obtained for the permutations of any set of the form {1,...,m}, e.g., {1,2,3} or {1,...,9}: In the first case we have P = (123,132,213,231,312,321) and P(4)-P(3) = 231 - 213 = 18 = a(3), and in the latter case P(4)-P(3) = 123456897 - 123456879 = 18, again. - _M. F. Hasler_, Jan 12 2013

Crossrefs

Cf. A030299, A219664.

Programs

  • Mathematica
    Take[Differences[Sort[FromDigits/@Permutations[Range[9]]]],70] (* Harvey P. Dale, Mar 31 2018 *)
  • PARI
    A209280_list(N=5)={my(v=vector(N,i,10^(N-i))~); v=vecsort(vector(N!,k,numtoperm(N,k)*v)); vecextract(v,"^1")-vecextract(v,"^-1")} \\ return the N!-1 first terms as a vector
  • PARI
    A209280(n)={if(a209280=='a209280 || #a209280A209280_list(A090529(n+1)));a209280[n]}

Formula

a(n) = A219664(n) = 9*A217626(n) (for n < 9!). - M. F. Hasler, Jan 12 2013
a(n) = a(m!-n) for any m < 10 such that n < m!.
Showing 1-3 of 3 results.

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

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