A302025 Permutation of natural numbers mapping ordinary factorization to "Ludic factorization": a(1) = 1, a(2n) = 2*a(n), a(A003961(n)) = A269379(a(n)).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 23, 20, 27, 22, 25, 24, 19, 26, 21, 28, 29, 30, 37, 32, 39, 34, 35, 36, 41, 46, 63, 40, 43, 54, 47, 44, 33, 50, 53, 48, 31, 38, 75, 52, 61, 42, 65, 56, 99, 58, 67, 60, 71, 74, 57, 64, 95, 78, 77, 68, 135, 70, 83, 72, 89, 82, 51, 92, 59, 126, 91, 80, 45, 86, 97, 108, 155, 94, 147, 88

Offset

1,2

Comments

See comments and examples in A302032 to see how Ludic factorization proceeds.

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences that are permutations of the natural numbers

Index entries for sequences computed from indices in prime factorization

Index entries for sequences generated by sieves

Formula

a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A269379(a(A064989(2n+1))).

a(n) = A269171(A250245(n)).

a(n) = A269387(A156552(n)).

Prog

(PARI)
\\ With A269379 precomputed:
A064989(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f)};
A302025(n) = if(1==n, n, if(!(n%2), 2*A302025(n/2), A269379(A302025(A064989(n)))));
(Scheme, with memoization-macro definec)
(definec (A302025 n) (cond ((= 1 n) n) ((even? n) (* 2 (A302025 (/ n 2)))) (else (A269379 (A302025 (A064989 n))))))

Crossrefs

Cf. A302026 (inverse permutation).

Cf. A156552, A250245, A269171, A269387 (similar or related permutations).

Cf. A003961, A064989, A269379.

Sequence in context: A255407 A269171 A269395 * A269396 A255408 A269172

Adjacent sequences: A302022 A302023 A302024 * A302026 A302027 A302028

Keyword

nonn

Author

Antti Karttunen, Apr 03 2018

Status

approved