A249745 Permutation of natural numbers: a(n) = (1 + A064989(A007310(n))) / 2.

1, 2, 3, 4, 6, 7, 9, 10, 5, 12, 15, 8, 16, 19, 21, 22, 13, 24, 11, 27, 30, 17, 31, 34, 36, 18, 37, 40, 20, 42, 28, 26, 45, 49, 51, 52, 54, 55, 29, 33, 25, 14, 57, 64, 43, 66, 69, 39, 35, 70, 75, 44, 76, 48, 79, 82, 61, 84, 23, 87, 90, 47, 46, 91, 96, 97, 99, 58, 56, 60, 100, 62, 73, 72, 106, 112, 114, 115, 65, 117, 120, 38, 94, 121

Offset: 1

Author

Antti Karttunen, Nov 23 2014

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A249746.

Row 2 of A251721.

Cf. A007310, A048673, A064989, A249823, A249735.

Programs

Mathematica

a249745[n_Integer] := Module[{f, p, a064989, a007310, a},
  f[x_] := Transpose@FactorInteger[x];
  p[x_] := Which[
    x == 1, 1,
    x == 2, 1,
    True, NextPrime[x, -1]];
  a064989[x_] := Times @@ Power[p /@ First[f[x]], Last[f[x]]];
  a007310[x_] := Select[Range[x], MemberQ[{1, 5}, Mod[#, 6]] &];
  a[x_] := (1 + a064989 /@ a007310[x])/2;
a[n]]; a249745[252] (* Michael De Vlieger, Dec 18 2014, after Harvey P. Dale at A007310 *)

PARI

A249745(n)=A064989(A007310(n))\2+1 \\ M. F. Hasler, Jan 19 2016

Scheme

(define (A249745 n) (/ (+ 1 (A064989 (A007310 n))) 2))

Formula

a(n) = (A064989(A007310(n)) + 1) / 2.

a(n) = A048673(A249823(n)), as a composition of related permutations.

A007310(n) = A249735(a(n)) for all n >= 1. (This is the permutation which sorts the terms of A249735 into an ascending order, as they occur in A007310.)