cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A269172 Permutation of natural numbers: a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A250469(a(A269380(2n+1))).

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 25, 20, 21, 22, 19, 24, 23, 26, 27, 28, 29, 30, 49, 32, 33, 34, 35, 36, 31, 50, 39, 40, 37, 42, 41, 44, 45, 38, 43, 48, 55, 46, 51, 52, 47, 54, 121, 56, 57, 58, 77, 60, 53, 98, 63, 64, 65, 66, 59, 68, 69, 70, 61, 72, 169, 62, 75, 100, 67, 78, 85, 80, 81
Offset: 1

Views

Author

Antti Karttunen, Mar 03 2016

Keywords

Links

Crossrefs

Inverse: A269171.
Cf. A000035, A003309, A008578, A083221, A250469, A260738, A260739, A269380.
Related or similar permutations: A260741, A260742, A269356, A269358, A255422.
Cf. also A269394 (a(3n)/3) and A269396.
Differs from A255408 for the first time at n=38, where a(38) = 50, while A255408(38) = 38.

Formula

a(1) = 1, then after for even n, a(n) = 2*a(n/2), and for odd n, A250469(a(A269380(n))).
a(1) = 1, for n > 1, a(n) = A083221(A260738(n), a(A260739(n))).
As a composition of other permutations:
a(n) = A252755(A269386(n)).
a(n) = A252753(A269388(n)).
Other identities. For all n >= 1:
A000035(a(n)) = A000035(n). [This permutation preserves the parity of n.]
a(A003309(n)) = A008578(n). [Maps Ludic numbers to noncomposites.]

A302034 A028234 analog for a factorization process based on the Ludic sieve (A255127); Discard all instances of the (smallest) Ludic factor A272565(n) from n.

Original entry on oeis.org

1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 7, 5, 1, 1, 9, 1, 5, 1, 11, 1, 3, 1, 13, 7, 7, 1, 15, 1, 1, 5, 17, 7, 9, 1, 19, 11, 5, 1, 21, 1, 11, 1, 23, 1, 3, 1, 25, 19, 13, 1, 27, 1, 7, 7, 29, 11, 15, 1, 31, 13, 1, 11, 33, 1, 17, 5, 35, 1, 9, 1, 37, 17, 19, 1, 39, 7, 5, 11, 41, 1, 21, 1, 43, 35, 11, 1, 45, 1, 23, 1, 47, 13, 3, 1, 49, 23, 25, 1, 51, 13, 13, 19
Offset: 1

Views

Author

Antti Karttunen, Apr 01 2018

Keywords

Comments

Iterating n, a(n), a(a(n)), a(a(a(n))), ..., until 1 is reached, and taking the Ludic factor (A272565) of each term gives a sequence of distinct Ludic numbers (A003309) in ascending order, while applying A302035 to the same terms gives the corresponding "exponents" of these Ludic factors in this nonstandard "Ludic factorization of n", unique for each natural number n >= 1. Permutation pair A302025/A302026 maps between this Ludic factorization and the ordinary prime factorization of n. See also comments and examples in A302032.

Links

Crossrefs

Cf. A003309, A255127, A260738, A260739, A269379, A269380, A302025, A302026, A302032, A302035.
Cf. A302036 (gives the positions of 1's).
Cf. also A028234, A302044.

Programs

  • PARI
    \\ Assuming A269379 and its inverse A269380 have been precomputed, then the following is reasonably fast:
A302034(n) = if(1==n,n,my(k=0); while((n%2), n = A269380(n); k++); n = (n/2^valuation(n, 2)); while(k>0, n = A269379(n); k--); (n));

Formula

For n > 1, a(n) = A269379^(r)(A000265(A260739(n))), where r = A260738(n)-1 and A269379^(r)(n) stands for applying r times the map x -> A269379(x), starting from x = n.
a(n) = A302025(A028234(A302026(n))).

A271419 If n is a ludic number, a(n)=0; if n is not a ludic number, a(n) is the ludic number that rejects n from the ludic number sieve.

Original entry on oeis.org

0, 0, 0, 2, 0, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 7, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 0, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 11, 2, 3, 2, 7, 2, 0, 2, 3, 2, 5, 2, 0, 2, 3, 2, 0, 2, 13, 2, 3, 2, 0, 2, 5, 2, 3, 2, 0, 2, 7
Offset: 1

Views

Author

Max Barrentine, Apr 07 2016

Keywords

Links

Crossrefs

Cf. A003309, A192607, A192490, A255127, A260738, A271420, A272565.
Cf. A264940 (analogous version for lucky numbers).

Programs

Formula

a(n) = (1-A192490(n)) * A272565(n). - Antti Karttunen, Sep 11 2016

A271420 Nonludicity of n.

Original entry on oeis.org

0, 0, 0, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 4, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 1, 3, 1, 2, 1, 0, 1, 5, 1, 2, 1, 4, 1, 0, 1, 2, 1, 3, 1, 0, 1, 2, 1, 0, 1, 6, 1, 2, 1, 0, 1, 3, 1, 2, 1, 0, 1, 4, 1
Offset: 1

Views

Author

Max Barrentine, Apr 07 2016

Keywords

Comments

If n is ludic, a(n)=0; if n is nonludic, a(n) is the step at which n is rejected from the ludic number sieve.

Links

Crossrefs

Cf. A003309, A192490, A192607, A255127, A271419.
Cf. A265859 (analogous version for lucky numbers).

Programs

Formula

a(n) = (1-A192490(n)) * A260738(n). - Antti Karttunen, Sep 11 2016
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