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 1-5 of 5 results.

A163896 Record values of A163894.

Original entry on oeis.org

0, 2, 4, 24, 33, 76, 390, 536, 1092, 6242, 17953, 137286, 143633
Offset: 0

Views

Author

Antti Karttunen, Sep 19 2009

Keywords

Crossrefs

a(n) = A163894(A163895(n)). See A163891, A163893, A163894, A163911, A163912.

A163895 Positions where A163894 obtains record values.

Original entry on oeis.org

0, 1, 2, 6, 12, 24, 72, 144, 288, 864, 1728, 5184, 10368
Offset: 0

Views

Author

Antti Karttunen, Sep 19 2009

Keywords

Comments

The ratios a(n+1)/a(n) from n>=1 onward start as 2,3,2,2,3,2,2,3,2,3,2,...

Crossrefs

See A163896, A309016.

A163355 Permutation of integers for constructing Hilbert curve in N x N grid.

Original entry on oeis.org

0, 1, 3, 2, 14, 15, 13, 12, 4, 7, 5, 6, 8, 11, 9, 10, 16, 19, 17, 18, 20, 21, 23, 22, 30, 29, 31, 28, 24, 25, 27, 26, 58, 57, 59, 56, 54, 53, 55, 52, 60, 61, 63, 62, 50, 51, 49, 48, 32, 35, 33, 34, 36, 37, 39, 38, 46, 45, 47, 44, 40, 41, 43, 42, 234, 235, 233, 232, 236, 239
Offset: 0

Views

Author

Antti Karttunen, Jul 29 2009

Keywords

Links

Crossrefs

Inverse: A163356. A163357 & A163359 give two variants of Hilbert curve in N x N grid. Cf. also A163332.
Second and third "powers": A163905, A163915.
In range [A000302(n-1)..A024036(n)] of this permutation, the number of cycles is given by A163910, number of fixed points seems to be given by A147600(n-1) (fixed points themselves: A163901). Max. cycle sizes is given by A163911 and LCM's of all cycle sizes by A163912.
See also: A000695, A163890, A163894, A163902-A163903, A163914, A163485, A302843, A302845.

Programs

  • Maple
    A057300 := proc(n)
    option remember;
    `if`(n=0, 0, procname(iquo(n, 4, 'r'))*4+[0, 2, 1, 3][r+1])
end proc:
A163355 := proc(n)
    option remember ;
    local d,base4,i,r ;
    if n <= 1 then
        return n ;
    end if;
    base4 := convert(n,base,4) ;
    d := op(-1,base4) ;
    i := nops(base4)-1 ;
    r := n-d*4^i ;
    if ( d=1 and type(i,even) ) or ( d=2 and type(i,odd)) then
        4^i+procname(A057300(r)) ;
    elif d= 3 then
        2*4^i+procname(A057300(r)) ;
    else
        3*4^i+procname(4^i-1-r) ;
    end if;
end proc:
seq(A163355(n),n=0..100) ; # R. J. Mathar, Nov 22 2023
  • PARI
    A057300(n) = { my(t=1, s=0); while(n>0,  if(1==(n%4),n++,if(2==(n%4),n--)); s += (n%4)*t; n >>= 2; t <<= 2); (s); };
A163355(n) = if(!n,n,my(i = (#binary(n)-1)\2, f = 4^i, d = (n\f)%4, r = (n%f)); if(((1==d)&&!(i%2))||((2==d)&&(i%2)), f+A163355(A057300(r)), if(3==d,f+f+A163355(A057300(r)), (3*f)+A163355(f-1-r)))); \\ Antti Karttunen, Apr 14 2018

Formula

a(0) = 0, and given d=1, 2 or 3, then a((d*(4^i))+r)
= (4^i) + a(A057300(r)), if d=1 and i is even, or if d=2 and i is odd
= 2*(4^i) + a(A057300(r)), if d=3,
= 3*(4^i) + a((4^i)-1-r) in other cases.
From Alan Michael Gómez Calderón, May 06 2025: (Start)
a(3*A000695(n)) = 2*A000695(n);
a(3*(A000695(n) + 2^A000695(2*m))) = 2*(A000695(n) + 2^A000695(2*m)) for m >= 2;
a((2 + 16^n)*2^(-1 + 4*m)) = 4^(2*(n + m) - 1) + (11*16^m - 2)/3. (End)

Extensions

Links to further derived sequences added by Antti Karttunen, Sep 21 2009

A163890 Orbit size of n in permutation A163355.

Original entry on oeis.org

1, 1, 2, 2, 6, 3, 3, 6, 6, 6, 3, 3, 6, 3, 6, 3, 1, 3, 3, 3, 1, 1, 2, 2, 4, 2, 2, 4, 4, 2, 4, 2, 4, 8, 8, 4, 4, 2, 2, 4, 2, 2, 2, 2, 8, 8, 4, 4, 4, 4, 8, 8, 4, 2, 4, 2, 4, 8, 4, 8, 2, 2, 2, 2, 6, 6, 6, 6, 12, 6, 6, 12, 12, 12, 6, 6, 18, 18, 18, 6, 3, 3, 6, 6, 6, 3, 3, 6, 6, 6, 3, 3, 6, 3, 6, 3, 9, 18
Offset: 0

Views

Author

Antti Karttunen, Sep 19 2009

Keywords

Comments

Will all terms of A003586 eventually appear?

Links

Crossrefs

See A163891, A163892, A163894.

Programs

  • Scheme
    (define (A163890 n) (let loop ((i 1) (nn (A163355 n))) (cond ((= nn n) i) (else (loop (1+ i) (A163355 nn))))))

A163892 Distinct values in A163890 in the order of appearance.

Original entry on oeis.org

1, 2, 6, 3, 4, 8, 12, 18, 9, 16, 32, 24, 108, 36, 48, 54, 72, 64, 96, 192, 216, 324, 144, 162, 288, 576, 648, 384, 1944, 432, 864, 486, 972, 1296, 27, 768, 1152, 128, 5832, 1728, 1536, 3456, 2304
Offset: 0

Views

Author

Antti Karttunen, Sep 19 2009

Keywords

Comments

Probably a permutation of A003586 (A036561).

Crossrefs

a(n) = A163890(A163891(n)). See also A163891, A163893, A163894, A163912.
Showing 1-5 of 5 results.

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