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.

A023409 If any power of 2 ends with k 6's and 7's, they must be the first k terms of this sequence in reverse order.

Original entry on oeis.org

6, 7, 7, 7, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 7, 7, 6, 6, 7, 7, 7, 6, 6, 6, 6, 7, 6, 7, 7, 7, 7, 7, 6, 6, 6, 6, 7, 6, 7, 7, 6, 6, 6, 6, 7, 6, 7, 6, 6, 7, 6, 7, 7, 7, 6, 6, 6, 7, 6, 7, 7, 7, 6, 6, 6, 6, 6, 7, 6, 6, 6, 7, 7, 6, 7, 7, 6, 7, 7, 6, 7, 6, 6, 7, 7, 6, 7, 6, 7, 7, 6, 6, 7, 7, 6, 6, 7
Offset: 0

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Author

Keywords

Comments

From Robert Israel, Mar 30 2018: (Start)
a(0)=6. If the concatenation 6a(n)...a(0) (as a decimal number) is divisible by 2^(n+2) then a(n+1)=6, otherwise a(n+1)=7.
Pomerance (see link) shows the sequence is not eventually periodic. (End)

Crossrefs

Programs

  • Maple
    a[0]:= 6: v:= 6:
    for n from 1 to 100 do
      if 6*10^n+v mod 2^(n+1)=0 then a[n]:= 6 else a[n]:= 7 fi;
      v:= v + a[n]*10^n
    od:
    seq(a[i],i=0..100); # Robert Israel, Mar 30 2018

A053317 a(n) contains n digits (either '2' or '5') and is divisible by 2^n.

Original entry on oeis.org

2, 52, 552, 5552, 55552, 255552, 5255552, 55255552, 255255552, 2255255552, 22255255552, 222255255552, 5222255255552, 55222255255552, 255222255255552, 2255222255255552, 22255222255255552, 222255222255255552
Offset: 1

Views

Author

Henry Bottomley, Mar 06 2000

Keywords

Crossrefs

Programs

  • Maple
    A[1]:= 2:
    for n from 2 to 100 do
       if A[n-1] mod 2^n = 0 then A[n]:= A[n-1]+2*10^(n-1)
       else A[n]:= A[n-1]+5*10^(n-1)
    fi
    od:
    seq(A[i],i=1..100); # Robert Israel, Oct 27 2019
  • Mathematica
    Table[Select[FromDigits/@Tuples[{2,5},n],Divisible[#,2^n]&],{n,18}]//Flatten (* Harvey P. Dale, Oct 12 2022 *)

Formula

a(n) = a(n-1) + 10^(n-1)*(2 + 3*(a(n-1)/2^(n-1) mod 2)), i.e., a(n) ends with a(n-1); if a(n-1) is divisible by 2^n then a(n) begins with a 2, if not then a(n) begins with a 5.

Extensions

Formula corrected by Robert Israel, Oct 27 2019

A055880 Quotients arising from sequence A053317.

Original entry on oeis.org

1, 13, 69, 347, 1736, 3993, 41059, 215842, 498546, 2202398, 10866824, 54261537, 637482331, 3370498978, 7788765114, 34411960682, 169793870966, 847836388608, 4238615459929, 49803023550277, 263320090876701, 1323752940946163
Offset: 1

Views

Author

J. Lowell, Jul 15 2000

Keywords

Crossrefs

Formula

a(n) = A053317(n)/2^n - David Wasserman, Apr 28 2002

Extensions

More terms from David Wasserman, Apr 28 2002
Showing 1-3 of 3 results.