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

1,2

Links

Table of n, a(n) for n=1..72.

Index entries for sequences that are permutations of the natural numbers

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 *)

Prog

(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

Crossrefs

Maps fractions between A020652/A020653 and A020653/A020652.

See also A054429.

Sequence in context: A296007 A277437 A339380 * A276572 A363370 A330311

Adjacent sequences: A054427 A054428 A054429 * A054431 A054432 A054433

Keyword

nonn,easy

Author

Antti Karttunen

Status

approved