cp's OEIS Frontend

A246165 Permutation of natural numbers: a(1) = 1, a(n) = A064989(n)-th integer among those positive integers not occurring earlier in the sequence. [A064989(n) shifts the prime factorization of n one step right].

%I A246165 #14 Nov 02 2014 12:18:37
%S A246165 1,2,4,3,7,6,11,5,12,10,17,9,23,16,19,8,29,18,35,15,28,25,41,14,31,34,
%T A246165 30,24,51,27,59,13,44,43,47,26,67,52,58,22,77,42,83,38,49,61,89,21,70,
%U A246165 46,73,53,99,45,69,37,88,75,111,40,119,85,72,20,94,64,127,63,103,68,137,39,143,97,79,78,106,87,151,36
%N A246165 Permutation of natural numbers: a(1) = 1, a(n) = A064989(n)-th integer among those positive integers not occurring earlier in the sequence. [A064989(n) shifts the prime factorization of n one step right].
%C A246165 Terms at a(2^n) are: 1, 2, 3, 5, 8, 13, 20, 32, 48, 71, 105, 156, 236, 354, 542, 815, 1228, ...
%C A246165 Fixed points begin as: 1, 2, 6, 10, 18, 42, 92, 26372, ...
%H A246165 Antti Karttunen, <a href="/A246165/b246165.txt">Table of n, a(n) for n = 1..8192</a>
%H A246165 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A246165 By definition, a(1) = 1.
%e A246165 After that, for n = 2, when its prime factorization is shifted once right, results A064989(2) = 1, so we select the 1st of still unused positive natural numbers, which is 2, thus a(2) = 2.
%e A246165 For n = 3 = p_2 (3 is the second prime), when its prime factorization is shifted once right, results A064989(3) = 2 = p_1, so we select 2nd of still unused numbers, which is 4, thus a(3) = 4.
%e A246165 For n = 4, like for all powers of two, the result of right shifting is 1, so we select the smallest still unused number, which is 3, thus a(4) = 3.
%e A246165 For n = 5 = p_3, A064989(5) = 3 = p_2, so we select the 3rd smallest still unused number from [5, 6, 7, 8, ...] which is 7, thus a(5) = 7.
%o A246165 (Scheme, with defineperm1-macro from _Antti Karttunen_'s IntSeq-library)
%o A246165 (defineperm1 (A246165 n) (if (<= n 1) n (let loop ((i 1) (the-n-th-one (- (A064989 n) 1))) (cond ((not-lte? (A246166 i) n) (if (zero? the-n-th-one) i (loop (+ i 1) (- the-n-th-one 1)))) (else (loop (+ i 1) the-n-th-one))))))
%o A246165 ;; We consider a > b (i.e. not less than or equivalent to b) also in case a is nil.
%o A246165 ;; (Which is needed when using the stateful caching system used by defineperm1-macro):
%o A246165 (define (not-lte? a b) (cond ((not (number? a)) #t) (else (> a b))))
%Y A246165 Inverse: A246166.
%Y A246165 Similar permutations: A119435, A126917.
%Y A246165 Cf. A064989.
%K A246165 nonn
%O A246165 1,2
%A A246165 _Antti Karttunen_, Aug 17 2014