A237126 -id:A237126 - cp's OEIS frontend

A257734 Permutation of natural numbers: a(1) = 1, a(lucky(n)) = ludic(1+a(n-1)), a(unlucky(n)) = nonludic(a(n)), where lucky(n) = n-th lucky number A000959, unlucky(n) = n-th unlucky number A050505, and ludic = A003309, nonludic = A192607.

1, 4, 2, 9, 6, 16, 7, 12, 3, 26, 14, 20, 25, 8, 13, 38, 22, 31, 36, 15, 61, 21, 54, 33, 17, 45, 51, 24, 81, 32, 41, 73, 5, 48, 27, 62, 119, 69, 35, 105, 46, 57, 47, 96, 10, 65, 39, 82, 83, 151, 115, 92, 50, 135, 63, 76, 64, 124, 18, 86, 55, 106, 23, 108, 189, 146, 43, 118, 193, 68, 169, 84, 91, 100, 149, 85, 156, 28, 179, 111, 74, 136, 34

Offset: 1

Antti Karttunen, May 06 2015

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Inverse: A257733.
Cf. A000959, A050505, A003309, A109497, A145649, A192607.
Related or similar permutations: A237126, A255421, A257725, A257732.
Cf. also A256486, A256487.

a(1) = 1; for n > 1: if A145649(n) = 1 [i.e., if n is lucky], then a(n) = A003309(1+a(A109497(n)-1)), otherwise a(n) = A192607(a(n-A109497(n))).
As a composition of other permutations:
a(n) = A255421(A257732(n)).
a(n) = A237126(A257725(n)).

A266637 a(1) = 1; for n > 1, if A192490(2*n + 1) = 1 [when 2n+1 is a Ludic number] a(n) = A003309(1+a(A266350(n)-1)), otherwise a(n) = A192607(a(n-A266350(n))).

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 6, 11, 8, 9, 17, 13, 10, 37, 14, 12, 19, 23, 15, 25, 67, 16, 43, 27, 21, 29, 18, 52, 22, 181, 20, 30, 47, 34, 41, 24, 36, 77, 88, 26, 97, 59, 39, 53, 115, 32, 42, 407, 28, 70, 33, 224, 61, 31, 44, 64, 227, 49, 121, 89, 57, 35, 131, 51, 71, 101, 113, 38, 125, 79, 287, 55, 72, 91, 146, 46, 58, 1361

Offset: 1

Antti Karttunen, Jan 28 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..6121
Index entries for sequences that are permutations of the natural numbers

Inverse: A266638.
Cf. A003309, A192490, A192607, A266350.
Related or similar permutations: A237126, A266417.

a(1) = 1; for n > 1, if A192490(2*n + 1) = 1 [when 2n+1 is Ludic number] a(n) = A003309(1+a(A266350(n)-1)), otherwise a(n) = A192607(a(n-A266350(n))).
As a composition of related permutations:
a(n) = A237126(A266417(n)).

A255420 Ludic recurrence: Iterates of f(n) = A003309(n+1) starting from n=1.

Original entry on oeis.org

1, 2, 3, 5, 11, 37, 181, 1361, 13927, 183871, 3005533, 59045717

Offset: 0

Antti Karttunen, Feb 23 2015

Donovan Johnson, Ludic numbers computed up to A003309(1236290) = 23000711

Cf. A000225, A003309, A007097, A237126, A255421.

a255420 n = a255420_list !! n
a255420_list = iterate (a003309 . (+ 1)) 1
-- Reinhard Zumkeller, Feb 25 2015

a(0) = 1; for n >= 1: a(n) = A003309(1+a(n-1)).
Other identities. For all n >= 0:
a(n) = A237126(A000225(n+1)).
a(n) = A255421(A007097(n)).

A266419 Odd nonludic numbers.

Original entry on oeis.org

9, 15, 19, 21, 27, 31, 33, 35, 39, 45, 49, 51, 55, 57, 59, 63, 65, 69, 73, 75, 79, 81, 85, 87, 93, 95, 99, 101, 103, 105, 109, 111, 113, 117, 123, 125, 129, 133, 135, 137, 139, 141, 145, 147, 151, 153, 155, 159, 163, 165, 167, 169, 171, 177, 183, 185, 187, 189, 191, 195, 197, 199, 201, 203, 205, 207, 213, 215

Offset: 1

Antti Karttunen, Jan 28 2016

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10220

Intersection of A005408 and A192607.
Cf. A192490, A266410, A237126.
Cf. also A071904, A266420.

Other identities. For all n >= 1:

a(n) = 1 + 2*A266410(n).

cp's OEIS Frontend

A257734 Permutation of natural numbers: a(1) = 1, a(lucky(n)) = ludic(1+a(n-1)), a(unlucky(n)) = nonludic(a(n)), where lucky(n) = n-th lucky number A000959, unlucky(n) = n-th unlucky number A050505, and ludic = A003309, nonludic = A192607.

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A266637 a(1) = 1; for n > 1, if A192490(2*n + 1) = 1 [when 2n+1 is a Ludic number] a(n) = A003309(1+a(A266350(n)-1)), otherwise a(n) = A192607(a(n-A266350(n))).

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A255420 Ludic recurrence: Iterates of f(n) = A003309(n+1) starting from n=1.

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A266419 Odd nonludic numbers.

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