A245709 Fixed points of A245705 and A245706.

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 40, 43, 48, 53, 64, 80, 86, 96, 106, 128, 160, 172, 192, 212, 249, 256, 320, 344, 384, 417, 424, 498, 512, 640, 688, 768, 834, 848, 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

Offset

1,2

Comments

The odd terms less than 2^25 are: 1, 3, 5, 43, 53, 249, 417, 1321, 5545, 6827, 7081, 8535, 1485465, 1876261, 3298409, 13937375.

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)).

Links

Antti Karttunen, Table of n, a(n) for n = 1..230

Prog

(PARI)
isA245709(n) = (A245705(n) == n);
i=0; for(n=1, 2^20, if(isA245709(n), i++; write("b245709.txt", i, " ", n)))
\\ Alternative implementation, based on given conjecture:
isA245709v2(n) = (A245608(n) == A245708(n));
i=0; for(n=1, 2^25, if(isA245709v2(n), i++; write("b245709v2.txt", i, " ", n)))
(Scheme, with Antti Karttunen's IntSeq-library, two alternative implementations)
(define A245709 (FIXED-POINTS 1 1 A245705))
(define A245709 (MATCHING-POS 1 1 (lambda (k) (= (A245608 k) (A245708 k)))))

Crossrefs

A000079 is a subsequence.

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

Sequence in context: A015702 A362127 A364960 * A364565 A364548 A364544

Adjacent sequences: A245706 A245707 A245708 * A245710 A245711 A245712

Keyword

nonn

Author

Antti Karttunen, Jul 30 2014

Status

approved