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

Author

Antti Karttunen, Jul 30 2014

Keywords

• nonn

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

Crossrefs

A000079 is a subsequence.

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

Programs

PARI

isA245709(n) = (A245705(n) == n);

PARI

\\ Alternative implementation, based on given conjecture:
isA245709v2(n) = (A245608(n) == A245708(n));

Scheme

;; With Antti Karttunen's IntSeq-library.
(define A245709 (FIXED-POINTS 1 1 A245705))

Scheme

;; With Antti Karttunen's IntSeq-library.
(define A245709 (MATCHING-POS 1 1 (lambda (k) (= (A245608 k) (A245708 k)))))