A054430 Simple self-inverse permutation of natural numbers: List each clump of phi(n) numbers (starting from phi(2) = 1) in reverse order.

1, 3, 2, 5, 4, 9, 8, 7, 6, 11, 10, 17, 16, 15, 14, 13, 12, 21, 20, 19, 18, 27, 26, 25, 24, 23, 22, 31, 30, 29, 28, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 45, 44, 43, 42, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 63, 62, 61, 60, 59, 58, 71, 70, 69, 68, 67, 66, 65, 64, 79

Offset: 1

Author

Antti Karttunen

Keywords

• nonn
• easy

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Maps fractions between A020652/A020653 and A020653/A020652.

See also A054429.

Programs

Maple

ReverseNextPhi_n_elements_permutation(30); with(numtheory,phi); ReverseNextPhi_n_elements_permutation := proc(u) local m,a,n,k,i; a := []; k := 0; for n from 2 to u do m := k + phi(n); for i from 1 to phi(n) do a := [op(a),m]; m := m-1; k := k+1; od; od; RETURN(a); end;

Mathematica

A[u_]:=Block[{m, a={}, n, k=0, i}, For[n=2, n<=u, n++, m=k + EulerPhi[n]; For[i=1, i<=EulerPhi[n], i++, AppendTo[a, m]; m=m - 1; k = k + 1]]; Return [a]]; A[30] (* Indranil Ghosh, May 23 2017, translated from MAPLE code *)
Reverse/@TakeList[Range[200],EulerPhi[Range[2,20]]]//Flatten (* Harvey P. Dale, Oct 19 2022 *)

Python

from sympy import totient
def A(u):
    a=[]
    k=0
    for n in range(2, u + 1):
        m=k + totient(n)
        for i in range(1, totient(n) + 1):
            a+=[m,]
            m-=1
            k+=1
    return a
print(A(30)) # Indranil Ghosh, May 23 2017, translated from MAPLE code