A227413 -id:A227413 - cp's OEIS frontend

A245614 Permutation of natural numbers: a(1)=1; thereafter, if n is k-th number whose greatest prime factor has an odd index [i.e., n = A244991(k)], a(n) = A026424(a(k)), otherwise, when n is k-th number whose greatest prime factor has an even index [i.e., n = A244990(1+k)], a(n) = A028260(1+a(k)).

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

Offset: 1

Antti Karttunen, Jul 27 2014

This shares with the permutation A122111 the property that each term of A244990 is mapped to a unique term of A028260 and each term of A244991 is mapped to a unique term of A026424.

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

Inverse: A245613.
Cf. A026424, A028260, A066829, A244988, A244989, A244990, A244991, A244992, A122111.
Similar permutations: A244321, A244322, A245604, A227413, A237126, A243288, A243344, A243346, A245606.

a(1) = 1, and for n > 1, if A244992(n) = 1, a(n) = A026424(a(A244989(n))), otherwise a(n) = A028260(1+a(A244988(n)-1)).
As a composition of related permutations:
a(n) = A245604(A244321(n)).
For all n >= 1, A244992(n) = A066829(a(n)).

A246346 Positions of records in A135141.

Original entry on oeis.org

1, 2, 3, 5, 8, 10, 15, 18, 25, 28, 38, 42, 55, 60, 77, 84, 105, 115, 140, 152, 183, 198, 235, 253, 298, 320, 372, 399, 462, 494, 566, 605, 692, 736, 838, 891, 1007, 1072, 1205, 1280, 1432, 1521, 1698, 1800, 2002, 2120, 2352, 2488, 2755, 2910, 3210, 3387, 3731, 3934, 4322, 4552, 4990, 5250

Offset: 1

Antti Karttunen, Aug 27 2014

nonn

Bisection 2, 5, 10, 18, 28, 42, ... seems to give the positions of records in A246348 after the initial positions: 1, 2, 3, 5, 10, 18, 28, 42, ...

This easily follows from the pattern present in A246347, as from its fourth term onward, each two successive new records appear to have the same binary width.

Antti Karttunen, Table of n, a(n) for n = 1..112

A246347 gives the corresponding values.

Cf. A135141, A227413, A246348.

PARI
```
\\ See code in A246348.
```

; with Antti Karttunen's IntSeq-library
(define A246346 (RECORD-POS 1 1 A135141))

a(n) = A227413(A246347(n)).

A252758 Permutation of natural numbers: a(1) = 1, a(2n) = A251726(a(n)), a(2n+1) = A251727(a(n)).

Original entry on oeis.org

1, 2, 10, 3, 14, 12, 38, 4, 20, 17, 44, 15, 40, 61, 92, 5, 22, 25, 57, 21, 51, 72, 102, 18, 46, 64, 94, 108, 132, 191, 182, 6, 26, 29, 60, 35, 68, 101, 124, 27, 58, 85, 116, 135, 152, 221, 198, 23, 52, 75, 106, 115, 138, 193, 184, 239, 206, 311, 242, 499, 333, 467, 318, 7, 28, 36, 69, 43, 76, 107, 130, 54, 87, 127, 145, 217, 196, 283, 231, 37

Offset: 1

Antti Karttunen, Jan 02 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..959
Index entries for sequences that are permutations of the natural numbers

Inverse: A252757.
Similar permutations: A243288, A227413, A237126.
Cf. A251726, A251727.

a(1) = 1, a(2n) = A251726(a(n)), a(2n+1) = A251727(a(n)).

cp's OEIS Frontend

A245614 Permutation of natural numbers: a(1)=1; thereafter, if n is k-th number whose greatest prime factor has an odd index [i.e., n = A244991(k)], a(n) = A026424(a(k)), otherwise, when n is k-th number whose greatest prime factor has an even index [i.e., n = A244990(1+k)], a(n) = A028260(1+a(k)).

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A246346 Positions of records in A135141.

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Formula

A252758 Permutation of natural numbers: a(1) = 1, a(2n) = A251726(a(n)), a(2n+1) = A251727(a(n)).

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