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A364576 Starting from k=1, each subsequent term is the next larger odd k such that A156552(k) < k and the ratio A156552(k)/k is nearer to 1.0 than for any previous k in the sequence.

%I A364576 #16 Aug 06 2023 17:49:45
%S A364576 1,3,5,21,323,66297,139965,263375,264845,528581
%N A364576 Starting from k=1, each subsequent term is the next larger odd k such that A156552(k) < k and the ratio A156552(k)/k is nearer to 1.0 than for any previous k in the sequence.
%C A364576 All the odd fixed points of map n -> A005940(n) [and its inverse, map n -> A005941(n)] are included in this sequence. This includes both the known odd fixed points, 1, 3 and 5 (see A029747), and any additional hypothetical odd composites that would satisfy the condition n == A005940(n).
%C A364576 This is a subsequence of A364561, so the comments given in A364564 apply also here.
%e A364576        k  A156552(k)    A156552(k)/k  k-(1+A156552(k)) factorization of k
%e A364576        1:       0         0                0
%e A364576        3:       2         0.6666667        0
%e A364576        5:       4         0.8              0
%e A364576       21:      18         0.8571429        2           (3 * 7)
%e A364576      323:     320         0.9907121        2           (17 * 19)
%e A364576    66297:   65714         0.9912062      582           (3 * 7^2 * 11 * 41)
%e A364576   139965:  139306         0.9952917      658           (3 * 5 * 7 * 31 * 43)
%e A364576   263375:  262364         0.9961614     1010           (5^3 * 7^2 * 43)
%e A364576   264845:  264244         0.9977307      600           (5 * 7^2 * 23 * 47)
%e A364576   528581:  528576         0.9999905        4           (17^2 * 31 * 59).
%Y A364576 Subsequence of A364561.
%Y A364576 Cf. A005940, A005941, A029747, A156552.
%Y A364576 Cf. also A364551, A364564, A364572.
%K A364576 nonn,more
%O A364576 1,2
%A A364576 _Antti Karttunen_, Aug 06 2023