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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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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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)

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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

A053378 a(n) contains n digits (either '5' or '8') and is divisible by 2^n.

Original entry on oeis.org

8, 88, 888, 5888, 85888, 885888, 8885888, 58885888, 558885888, 8558885888, 58558885888, 858558885888, 5858558885888, 85858558885888, 585858558885888, 5585858558885888, 55585858558885888, 855585858558885888
Offset: 1

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Author

Henry Bottomley, Mar 06 2000

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Formula

a(n)=a(n-1)+10^(n-1)*(8-3*[a(n-1)/2^(n-1) mod 2]) i.e. a(n) ends with a(n-1); if (n-1)-th term is divisible by 2^n then n-th term begins with an 8, if not then n-th term begins with a 5.
Showing 1-2 of 2 results.