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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A092697 For 1 <= n <= 9, a(n) = least number m such that the product n*m is obtained merely by shifting the rightmost digit of m to the left end (a finite sequence).

Original entry on oeis.org

1, 105263157894736842, 1034482758620689655172413793, 102564, 142857, 1016949152542372881355932203389830508474576271186440677966, 1014492753623188405797, 1012658227848, 10112359550561797752808988764044943820224719
Offset: 1

Views

Author

Lekraj Beedassy, Aug 21 2004; corrected Dec 17 2004

Keywords

Comments

This is the least n-parasitic number. A k-parasitic number (where 1 <= k <= 9) is one such that when it is multiplied by k, the product obtained is merely its rightmost digit transferred in front at the leftmost end.

Examples

			102564 is 4-parasitic because we have 102564*4=410256.
For n=5: 142857*5=714285. [Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009]

References

  • C. A. Pickover, Wonders of Numbers, Chapter 28, Oxford Univ. Press UK 2000.

Links

Crossrefs

Cf. A094676, A081463.
For other sequences with the same start, see A128857 and especially the cross-references in A097717.

Extensions

Edited by N. J. A. Sloane, Apr 13 2009
Corrected to set 5th term to 142857 as this is the least 5-parasitic number. Dzmitry Paulenka (pavlenko(AT)tut.by), Aug 09 2009
a(9) added by Ian Duff, Jan 03 2012
Incorrect formula removed by Alois P. Heinz, Feb 18 2020

A081461 Consider the mapping f(a/b) = (a^2+b^3)/(a^3+b^2) from rationals to rationals. Starting with 1/2 (a=1, b=2) and applying the mapping to each new (reduced) rational number gives 1/2, 9/5, 103/377, ... . Sequence gives values of the numerators.

Original entry on oeis.org

1, 9, 103, 26796621, 236092315725004393, 3561970421302126514421966146019939188025056477849165490630219227287
Offset: 1

Views

Author

Amarnath Murthy, Mar 22 2003

Keywords

Comments

For the mapping g(a/b) = (a^2+b)/(a+b^2), starting with 1/2 the same procedure leads to the periodic sequence 1/2, 3/5, 1/2, 3/5, ...

Crossrefs

Cf. A000058, A081462, A081463, A081465.

Programs

  • Mathematica
    nxt[{a_,b_}]:=Module[{frac=(a^2+b^3)/(a^3+b^2)},{Numerator[frac], Denominator[ frac]}]; Transpose[NestList[nxt,{1,2},5]][[1]] (* Harvey P. Dale, Nov 09 2011 *)
  • PARI
    {r=1/2; for(n=1,7,a=numerator(r); b=denominator(r); print1(a,","); r=(a^2+b^3)/(a^3+b^2))}

Extensions

Edited and extended by Klaus Brockhaus, Mar 28 2003

A087502 Smallest positive integer which when written in base n is doubled when the last digit is put first.

Original entry on oeis.org

32, 18, 8, 10993850, 2129428800, 21, 5064320, 105263157894736842, 40, 64609423538, 5712, 65, 58774271029236501660840264682112, 67650, 96, 833, 586081355679130611935159482937228562988190880, 133
Offset: 3

Views

Author

Pontus von Brömssen, Sep 10 2003

Keywords

Comments

a(n) is the smallest integer of the form x*(n^d-1)/(2n-1) for integer x and d, where 1 < x < n and d > 1. x is the last digit and d is the number of digits of a(n) in base n. - Pontus von Brömssen, Jan 06 2019

Examples

			a(10) = 105263157894736842 because 2*105263157894736842 = 210526315789473684 and no smaller number has this property. (Leading zeros are not allowed, otherwise 2*052631578947368421 = 105263157894736842 would be a smaller solution.)

Links

Crossrefs

See A158877 for these numbers written in base n. Cf. A023094, A034089, A081463, A087502.

Programs

  • Maple
    A087502 := proc(n) local d,a; d := 1; a := n; while a>=n do d := d+1; a := denom((2^d-1)/(2*n-1)); od; return(max(2,a)*(n^d-1)/(2*n-1)); end proc;
Showing 1-3 of 3 results.

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

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