A342131 -id:A342131 - cp's OEIS frontend

A367286 Inverse of A342131.

0, 2, 1, 4, 6, 3, 8, 10, 5, 12, 14, 7, 16, 18, 9, 20, 22, 11, 24, 26, 13, 28, 30, 15, 32, 34, 17, 36, 38, 19, 40, 42, 21, 44, 46, 23, 48, 50, 25, 52, 54, 27, 56, 58, 29, 60, 62, 31, 64, 66, 33, 68, 70, 35, 72, 74, 37, 76, 78, 39, 80, 82, 41, 84, 86, 43, 88, 90, 45, 92, 94, 47

Offset: 0

Philippe Deléham, Nov 12 2023

Permutation of the nonnegative numbers.

Paolo Xausa, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (0,0,2,0,0,-1).
Index entries for sequences that are permutations of the nonnegative integers

Cf. A006369, A342131.

LinearRecurrence[{0,0,2,0,0,-1},{0,2,1,4,6,3},100] (* Paolo Xausa, Nov 14 2023 *)

a(3*n) = 4*n, a(3*n+1) = 4*n+2, a(3*n+2) = 2*n+1.
a(n) = 2*a(n-3) - a(n-6) for n >= 6.
a(n) = A006369(n+1) - 1.
G.f.: x*(2+x+4*x^2+2*x^3+x^4)/(1-x^3)^2.
E.g.f.: exp(-x/2)*(exp(3*x/2)*(10*x + 1) + (2*x - 1)*cos(sqrt(3)*x/2) + sqrt(3)*(3 - 2*x)*sin(sqrt(3)*x/2))/9. - Stefano Spezia, Nov 12 2023

A340709 Let k = n/2 + floor(n/4) if n is even, otherwise (3n+1)/2; then a(n) = A093545(k).

Original entry on oeis.org

0, 1, 2, 3, 5, 4, 7, 6, 10, 8, 12, 9, 15, 11, 17, 13, 20, 14, 22, 16, 25, 18, 27, 19, 30, 21, 32, 23, 35, 24, 37, 26, 40, 28, 42, 29, 45, 31, 47, 33, 50, 34, 52, 36, 55, 38, 57, 39, 60, 41, 62, 43, 65, 44, 67, 46, 70, 48, 72, 49, 75, 51, 77, 53, 80, 54, 82, 56, 85, 58, 87

Offset: 0

Thomas Scheuerle, Jan 16 2021

This is a permutations of the nonnegative integers.
A093545 is the inverse of A340615.
Some of the cycles of this permutation are: (0),(1),(2),(3),(5 4),(7 6),(10 12 15 13 11 9 8),(17 14),(20 25 21 18 22 27 23 19 16),... .
A340615 and A342131 are permutations, constructed by a small modification of Collatz function (A014682). This sequence relates these permutations which each other: A340615(a(n)) = A342131(n).

Index entries for sequences that are permutations of the nonnegative integers.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,1,0,1,0,0,0,-1).
Index entries for sequences related to 3x+1 (or Collatz) problem.

Cf. A014682, A340615, A093545, A342131.

function a = A340709(max_n)
    for n = 1:max_n*10
        k = (n-1)+floor(((n-1)+1)/5);
        m = n-1;
        if floor(k/2) == k/2
            A340615(n) = k/2;
        else
            A340615(n) = (k*3+1)/2;
        end
        if floor(m/2) == m/2
            b(n) = m/2+floor(m/4);
        else
            b(n) = (m*3+1)/2;
        end
    end
    for n = 1:(length(A340615)/10)
        a(n) = find(A340615==b(n))-1;
    end
end

a(4*m) = 5*m.
a(2+4*m) = 2+5*m.
a(1+6*m) = 1+5*m.
a(3+6*m) = 3+5*m.
a(4+6*m) = 4+5*m.
a(n) = -2*a(n-1) - 3*a(n-2) - 4*a(n-3) - 4*a(n-4) - 4*a(n-5) - 3*a(n-6) - 2*a(n-7) - a(n-8) + 25n - 101 for n >= 8.
a(n) = A093545(A342131(n)).
G.f.: x*(1 + 2*x + 3*x^2 + 5*x^3 + 3*x^4 + 5*x^5 + 2*x^6 + 3*x^7 + x^8)/(1 - x^4 - x^6 + x^10). - Stefano Spezia, Mar 01 2021

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A367286 Inverse of A342131.

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