This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A249746 #32 Aug 07 2016 20:43:40
%S A249746 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,
%T A249746 20,31,39,21,23,92,40,24,49,25,27,82,48,28,209,30,45,52,33,63,62,54,
%U A249746 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
%N A249746 Permutation of natural numbers: a(n) = A126760(A249735(n)) = A249824(A064216(n)).
%C A249746 Permutation obtained from the odd bisection of A003961 (or from the odd bisection of A048673).
%H A249746 Antti Karttunen, <a href="/A249746/b249746.txt">Table of n, a(n) for n = 1..10000</a>
%H A249746 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A249746 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.]
%F A249746 a(n) = A126760(A249735(n)). - _Antti Karttunen_, Jul 25 2016
%F A249746 As a composition of related permutations:
%F A249746 a(n) = A249824(A064216(n)).
%F A249746 Other identities. For all n >= 1:
%F A249746 A249735(n) = A007310(a(n)).
%F A249746 a(3n-1) = A273669(a(n)) and a(A254049(n)) = A273664(a(n)). - _Antti Karttunen_, Aug 07 2016
%e A249746 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.
%t A249746 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 *)
%o A249746 (Scheme)
%o A249746 (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)))))
%Y A249746 Inverse: A249745.
%Y A249746 Row 2 of A251722.
%Y A249746 Cf. A003961, A007310, A048673, A084967, A126760, A249735, A064216, A249824.
%Y A249746 Cf. also A273664, A273669.
%K A249746 nonn
%O A249746 1,2
%A A249746 _Antti Karttunen_, Nov 23 2014