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A332897 a(1) = 0, a(2) = 1, and for n > 2, a(n) = a(A332893(n)) + [n == 1 (mod 4)].

%I A332897 #9 Mar 04 2020 18:09:03
%S A332897 0,1,1,1,2,1,2,1,2,2,3,1,3,2,1,1,4,2,4,2,3,3,5,1,3,3,1,2,5,1,6,1,4,4,
%T A332897 1,2,6,4,2,2,7,3,7,3,2,5,8,1,4,3,3,3,8,1,2,2,5,5,9,1,9,6,2,1,4,4,10,4,
%U A332897 6,1,11,2,10,6,2,4,5,2,12,2,2,7,13,3,5,7,4,3,11,2,1,5,7,8,3,1,12,4,3,3,13,3,14,3,2
%N A332897 a(1) = 0, a(2) = 1, and for n > 2, a(n) = a(A332893(n)) + [n == 1 (mod 4)].
%C A332897 Starting from x=n, iterate the map x -> A332893(x) which divides even numbers by 2, and for odd n changes every 4k+1 prime in their prime factorization to 4k+3 prime and vice versa (except 3 -> 2), like in A332819. a(n) counts the numbers of the form 4k+1 encountered until 1 has been reached, which is also included in the count when n > 1. This count includes also n itself when it is of the form 4k+1 (A016813) and larger than 1.
%H A332897 Antti Karttunen, <a href="/A332897/b332897.txt">Table of n, a(n) for n = 1..65537</a>
%F A332897 a(1) = 0, a(2) = 1, and for n > 2, a(n) = a(A332893(n)) + [n == 1 (mod 4)].
%F A332897 a(n) = A000120(A332895(n)).
%o A332897 (PARI) A332897(n) = if(n<=2,n-1,A332897(A332893(n)) + (1==(n%4)));
%Y A332897 Cf. A016813, A332893, A332895, A332898, A332899.
%Y A332897 Cf. also A292375.
%K A332897 nonn
%O A332897 1,5
%A A332897 _Antti Karttunen_, Mar 04 2020