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 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)). 9
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified July 29 05:59 EDT 2021. Contains 346340 sequences. (Running on oeis4.)