cp's OEIS Frontend

A249818 Permutation of natural numbers: a(1) = 1, a(n) = A246278(A055396(n),A078898(n)).

%I A249818 #21 Jan 09 2016 18:02:40
%S A249818 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,27,22,23,24,25,26,
%T A249818 21,28,29,30,31,32,45,34,35,36,37,38,33,40,41,42,43,44,81,46,47,48,49,
%U A249818 50,75,52,53,54,125,56,63,58,59,60,61,62,39,64,55,66,67,68,135,70,71,72,73,74,51,76,77,78,79,80,99,82,83,84,175,86,105
%N A249818 Permutation of natural numbers: a(1) = 1, a(n) = A246278(A055396(n),A078898(n)).
%C A249818 a(n) tells which number in square array A246278 is at the same position where n is in array A083221, the sieve of Eratosthenes. As both arrays have even numbers as their topmost row and primes as their leftmost column, both sequences are among the fixed points of this permutation.
%C A249818 Equally: a(n) tells which number in array A246279 is at the same position where n is in the array A083140, as they are the transposes of above two arrays.
%H A249818 Antti Karttunen, <a href="/A249818/b249818.txt">Table of n, a(n) for n = 1..10000</a>
%H A249818 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A249818 a(1) = 1, a(n) = A246278(A055396(n), A078898(n)).
%F A249818 a(1) = 1, a(n) = A246278(A055396(n), A249822(A055396(n), A246277(n))).
%F A249818 As a composition of other permutations:
%F A249818 a(1) = 1, and for n > 1, a(n) = 1 + A249816(n-1).
%F A249818 Other identities. For all n >= 1:
%F A249818 a(A005843(n)) = A005843(n) and a(A000040(n)) = A000040(n). [Fixes even numbers and primes, among other numbers. Cf. comments above].
%F A249818 A020639(a(n)) = A020639(n) and A055396(a(n)) = A055396(n). [Preserves the smallest prime factor of n].
%t A249818 lim = 87; a003961[p_?PrimeQ] := a003961[p] = Prime[PrimePi@ p + 1]; a003961[1] = 1; a003961[n_] :=  a003961[n] = Times @@ (a003961[First@ #]^Last@ # &) /@ FactorInteger@ n; a055396[n_] := PrimePi[FactorInteger[n][[1, 1]]]; a078898 = Block[{nn = 90, spfs}, spfs = Table[FactorInteger[n][[1, 1]], {n, nn}]; Table[Count[Take[spfs, i], spfs[[i]]], {i, nn}]]; a246278 = NestList[Map[a003961, #] &, Table[2 k, {k, lim}], lim]; Table[a246278[[a055396@ n, a078898[[n]]]], {n, 2, lim}]
%t A249818 (* _Michael De Vlieger_, Jan 04 2016, after _Harvey P. Dale_ at A055396 and A078898 *)
%o A249818 (define (A249818 n) (if (= 1 n) n (A246278bi (A055396 n) (A078898 n)))) ;; Code for A246278bi given in A246278.
%o A249818 ;; Alternatively:
%o A249818 (define (A249818 n) (if (= 1 n) n (A246278bi (A055396 n) (A249822bi (A055396 n) (A246277 n))))) ;; Code for A249822bi given in A249822.
%Y A249818 Inverse: A249817.
%Y A249818 There are three different "deep" versions of this permutation, recursing on values of A055396(n) and/or A078898(n), namely: A250246, A250248 and A250250.
%Y A249818 Other similar or related permutations: A249816.
%Y A249818 Cf. A000040, A005843, A020639, A055396, A078898, A083140, A083221, A246277, A246278, A246279, A249822.
%Y A249818 Differs from its inverse A249817 for the first time at n=33, where a(33) = 45, while A249817(33) = 39.
%K A249818 nonn
%O A249818 1,2
%A A249818 _Antti Karttunen_, Nov 06 2014