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A245709 Fixed points of A245705 and A245706.

%I A245709 #21 Apr 01 2025 17:51:40
%S A245709 1,2,3,4,5,6,8,10,12,16,20,24,32,40,43,48,53,64,80,86,96,106,128,160,
%T A245709 172,192,212,249,256,320,344,384,417,424,498,512,640,688,768,834,848,
%U A245709 996,1024,1280,1321,1376,1536,1668,1696,1992,2048,2560,2642,2752,3072,3336,3392,3984,4096,5120,5284,5504,5545,6144,6672,6784,6827,7081,7968,8192
%N A245709 Fixed points of A245705 and A245706.
%C A245709 The odd terms less than 2^25 are: 1, 3, 5, 43, 53, 249, 417, 1321, 5545, 6827, 7081, 8535, 1485465, 1876261, 3298409, 13937375.
%C A245709 Contains also all such numbers k that A245608(k) = A245708(k), because that condition implies that A245607(A245708(k)) = k = A245707(A245608(k)). Conjecture: contains no numbers outside of that set, that is, for all n, A245608(a(n)) = A245708(a(n)).
%H A245709 Antti Karttunen, <a href="/A245709/b245709.txt">Table of n, a(n) for n = 1..230</a>
%o A245709 (PARI)
%o A245709 isA245709(n) = (A245705(n) == n);
%o A245709 (PARI) \\ Alternative implementation, based on given conjecture:
%o A245709 isA245709v2(n) = (A245608(n) == A245708(n));
%o A245709 (Scheme)
%o A245709 ;; With _Antti Karttunen_'s IntSeq-library.
%o A245709 (define A245709 (FIXED-POINTS 1 1 A245705))
%o A245709 (Scheme)
%o A245709 ;; With _Antti Karttunen_'s IntSeq-library.
%o A245709 (define A245709 (MATCHING-POS 1 1 (lambda (k) (= (A245608 k) (A245708 k)))))
%Y A245709 A000079 is a subsequence.
%Y A245709 Cf. A245705, A245706, A245608, A245708, A029747, A244154.
%K A245709 nonn
%O A245709 1,2
%A A245709 _Antti Karttunen_, Jul 30 2014