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A245709 Fixed points of A245705 and A245706. 5

%I #14 Aug 18 2014 00:51:53

%S 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 172,192,212,249,256,320,344,384,417,424,498,512,640,688,768,834,848,

%U 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 Fixed points of A245705 and A245706.

%C 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 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 Antti Karttunen, <a href="/A245709/b245709.txt">Table of n, a(n) for n = 1..230</a>

%o (PARI)

%o isA245709(n) = (A245705(n) == n);

%o i=0; for(n=1, 2^20, if(isA245709(n), i++; write("b245709.txt", i, " ", n)))

%o \\ Alternative implementation, based on given conjecture:

%o isA245709v2(n) = (A245608(n) == A245708(n));

%o i=0; for(n=1, 2^25, if(isA245709v2(n), i++; write("b245709v2.txt", i, " ", n)))

%o (Scheme, with _Antti Karttunen_'s IntSeq-library, two alternative implementations)

%o (define A245709 (FIXED-POINTS 1 1 A245705))

%o (define A245709 (MATCHING-POS 1 1 (lambda (k) (= (A245608 k) (A245708 k)))))

%Y A000079 is a subsequence.

%Y Cf. A245705, A245706, A245608, A245708, A029747, A244154.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jul 30 2014

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