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.

A061147 Product of all distinct numbers formed by permuting digits of n.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 252, 403, 574, 765, 976, 1207, 1458, 1729, 40, 252, 22, 736, 1008, 1300, 1612, 1944, 2296, 2668, 90, 403, 736, 33, 1462, 1855, 2268, 2701, 3154, 3627, 160, 574, 1008, 1462, 44, 2430, 2944, 3478, 4032, 4606, 250, 765, 1300
Offset: 1

Views

Author

N. J. A. Sloane, May 30 2001

Keywords

Examples

			a(12) = 12*21 = 252.

Links

Crossrefs

Cf. A061378, A062003, A045876.

Programs

  • Mathematica
    Table[Times@@Union[FromDigits/@Permutations[IntegerDigits[n]]],{n,60}] (* Harvey P. Dale, Apr 06 2023 *)

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), May 30 2001

A062003 Product of the k numbers formed by cyclically permuting digits of n (where k = number of digits of n).

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 252, 403, 574, 765, 976, 1207, 1458, 1729, 40, 252, 22, 736, 1008, 1300, 1612, 1944, 2296, 2668, 90, 403, 736, 33, 1462, 1855, 2268, 2701, 3154, 3627, 160, 574, 1008, 1462, 44, 2430, 2944, 3478, 4032, 4606, 250
Offset: 0

Views

Author

Amarnath Murthy, May 30 2001

Keywords

Comments

Apparently some kind of distinctness is required, because n=11 (cyclically permuted again 11) is not translated to 11*11=121. - R. J. Mathar, Jun 13 2025

Examples

			a(14) = 14*41 = 574, a(100) = 100*010*001 = 1000, a(102) = 102*210*21 = 449820.

Crossrefs

Cf. A061147, A061378.

Programs

  • ARIBAS
    for k := 0 to 60 do st := itoa(k); m := 1; for i := 1 to length(st) do st := concat(st[1..length(st)-1],st[0]); m := m*atoi(st); end; write(m," "); end;

Extensions

Corrected and extended by Frank Ellermann and Klaus Brockhaus, Jun 03 2001

A179055 Numbers k such that the product of all numbers formed by cyclically permuting digits of k is a square.

Original entry on oeis.org

1, 4, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 243, 324, 432, 567, 675, 756, 1000, 1010, 1020, 1030, 1040, 1050, 1060, 1070, 1080, 1090, 1111, 1212, 1313, 1414, 1515, 1616, 1717, 1818, 1919, 2000, 2010, 2020, 2030, 2040, 2050, 2060, 2070, 2080, 2090, 2121, 2222, 2323, 2424
Offset: 1

Views

Author

Michel Lagneau, Jan 04 2011

Keywords

Examples

			756 is in the sequence because 756 * 567 * 675 = 289340100 = 17010^2.

Crossrefs

Cf. A061378 A062003 A061147.

Programs

  • Maple
    with(numtheory):for n from 1 to 4000 do:pp:=1:n0:=n:l:=length(n0) :ind:=0:for
  j from 1 to l do:s:=0:for m from 1 to l do:q:=n0:u:=irem(q, 10):v:=iquo(q, 10):n0:=v
  :s:=s+ u*10^m:od:s:=floor(s-u*10^l+u):n0:=s: pp:=pp*s:od:x:=sqrt(pp) :y:=floor(x):if
  x=y then printf(`%d, `, n): else fi :od:
  • Mathematica
    cycDigitPerms[n_Integer, b_:10] := Module[{list = {n}, digits = IntegerDigits[n, b], len, counter, holder, next}, len = Length[digits]; counter = 1; While[counter < len, holder = digits[[-1]]; digits = Drop[digits, -1]; digits = Insert[digits, holder, 1]; list = Append[list, FromDigits[digits, b]]; counter++]; Return[list]]; Select[Range[2000], IntegerQ[Sqrt[Times@@cycDigitPerms[#]]] &] (* Alonso del Arte, Jan 04 2011 *)
Showing 1-3 of 3 results.

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

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