A245608 -id:A245608 - cp's OEIS frontend

A245604 Permutation of natural numbers: a(1)=1, a(2n) = A026424(a(n)), a(2n+1) = A028260(1+a(n)).

1, 2, 4, 3, 6, 7, 10, 5, 9, 11, 15, 12, 16, 18, 24, 8, 14, 17, 22, 19, 25, 28, 35, 20, 26, 29, 36, 31, 39, 44, 55, 13, 21, 27, 34, 30, 38, 42, 51, 32, 40, 45, 56, 50, 60, 67, 81, 37, 46, 47, 57, 52, 62, 68, 82, 59, 65, 72, 86, 79, 93, 105, 121, 23, 33, 41, 49, 48, 58, 66, 77, 53, 64, 71, 85, 76, 90, 99, 111, 61

Offset: 1

Antti Karttunen, Jul 27 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences that are permutations of the natural numbers

Inverse: A245603.

Similar permutations: A143691, A244152, A244322, A245614, A245606, A245608.

a(1)=1, a(2n) = A026424(a(n)), a(2n+1) = A028260(1+a(n)).
As a composition of related permutations:
a(n) = A245614(A244322(n)).
For all n >= 1, A066829(a(n)) = 1 - A000035(n). [Permutation A143691 has the same property].
Equally, A066829(a(n)*a(n+1)) = 1 for all n.

A245709 Fixed points of A245705 and A245706.

Original entry on oeis.org

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

Antti Karttunen, Jul 30 2014

nonn

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)).

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

A000079 is a subsequence.

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

PARI
```
isA245709(n) = (A245705(n) == n);
```

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

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

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

cp's OEIS Frontend

A245604 Permutation of natural numbers: a(1)=1, a(2n) = A026424(a(n)), a(2n+1) = A028260(1+a(n)).

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A245709 Fixed points of A245705 and A245706.

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