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%I #14 Dec 13 2023 08:23:54
%S 1,2,3,4,5,6,9,8,10,12,7,18,15,16,20,24,25,14,27,36,30,32,21,40,48,50,
%T 28,54,45,72,11,60,64,42,80,96,75,100,56,108,35,90,81,144,22,120,63,
%U 128,84,160,192,150,135,200,112,216,70,180,49,162,33,288,44,240,126,256,125,168,320,384,225,300,105,270,400
%N Permutation of natural numbers: a(1) = 1, for n > 1, if n is an odd prime, a(n) = A003961(a(A000720(n))), otherwise a(n) = 2*a(n-A000720(n)).
%H Antti Karttunen, <a href="/A269847/b269847.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(1) = 1, and for n > 1, if n is an odd prime, a(n) = A003961(a(A000720(n))), otherwise [when n is 2 or composite] a(n) = 2*a(n-A000720(n)).
%F a(1) = 1; if n is an odd prime, a(n) = A003961(a(A026233(n))), else a(n) = A005843(a(A026233(n))).
%F Declarative definition:
%F a(1)=1, a(A065091(n)) = A003961(a(n+1)), a(A065090(n+1)) = 2*a(n).
%F As a composition of other permutations:
%F a(n) = A163511(A071574(n)).
%F Other identities. For all n >= 1:
%F a(A007097(n)) = A000040(n). [Maps the terms of primeth recurrence to primes.]
%o (Scheme, with memoization-macro definec)
%o (definec (A269847 n) (cond ((<= n 1) n) ((and (odd? n) (= 1 (A010051 n))) (A003961 (A269847 (A000720 n)))) (else (* 2 (A269847 (- n (A000720 n)))))))
%Y Inverse: A269848.
%Y Cf. A000040, A000720, A003961, A005843, A007097, A010051, A026233, A065090, A065091.
%Y Related or similar permutations: A071574, A163511, A246681, A257730, A269857.
%K nonn
%O 1,2
%A _Antti Karttunen_, Mar 06 2016
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