A249746 Permutation of natural numbers: a(n) = A126760(A249735(n)) = A249824(A064216(n)).

1, 2, 3, 4, 9, 5, 6, 12, 7, 8, 19, 10, 17, 42, 11, 13, 22, 26, 14, 29, 15, 16, 59, 18, 41, 32, 20, 31, 39, 21, 23, 92, 40, 24, 49, 25, 27, 82, 48, 28, 209, 30, 45, 52, 33, 63, 62, 54, 34, 109, 35, 36, 129, 37, 38, 69, 43, 68, 142, 70, 57, 72, 115, 44, 79, 46, 85, 292, 47, 50, 89, 74, 73, 202, 51, 53, 159, 87, 55, 99, 107, 56, 152, 58, 97, 192, 60

Offset: 1

Author

Antti Karttunen, Nov 23 2014

Keywords

• nonn

Comments

Permutation obtained from the odd bisection of A003961 (or from the odd bisection of A048673).

Examples

			a(5) = 9 because of the following. 2*A064216(5) = 2*4 = 8 = 2^3. We replace the prime factor 2 of 8 with the next prime 3 to get 3^3, then replace 3 with 5 to get 5^3 = 125. The smallest prime factor of 125 is 5. 125 is the 9th term of A084967: 5, 25, 35, 55, 65, 85, 95, 115, 125, ..., thus a(5) = 9.
		

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: A249745.

Row 2 of A251722.

Cf. A003961, A007310, A048673, A084967, A126760, A249735, A064216, A249824.

Cf. also A273664, A273669.

Programs

Mathematica

t = PositionIndex[FactorInteger[#][[1, 1]] & /@ Range[10^6]]; f[n_] := Times @@ Power[If[# == 1, 1, NextPrime@ #] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n; Flatten@ Map[Position[Lookup[t, FactorInteger[#][[1, 1]] ], #] &[f@ f[2 #]] &, Table[Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1], {n, 87}]] (* Michael De Vlieger, Jul 25 2016, Version 10 *)

Scheme

(define (A249746 n) (define (Ainv_of_A007310off0 n) (+ (* 2 (floor->exact (/ n 6))) (/ (- (modulo n 6) 1) 4))) (+ 1 (Ainv_of_A007310off0 (A003961 (+ n n -1)))))

Formula

a(n) = 1 + f(A003961(2n - 1)), where f(n) = 2*floor[n/6] + ((n mod 6)-1)/4. [Here 1 + f(A007310(n)) = n.]

a(n) = A126760(A249735(n)). - Antti Karttunen, Jul 25 2016

As a composition of related permutations:

a(n) = A249824(A064216(n)).

Other identities. For all n >= 1:

A249735(n) = A007310(a(n)).

a(3n-1) = A273669(a(n)) and a(A254049(n)) = A273664(a(n)). - Antti Karttunen, Aug 07 2016