The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A302026 Permutation of natural numbers mapping "Ludic factorization" to ordinary factorization: a(1) = 1, a(2n) = 2*a(n), a(A269379(n)) = A003961(a(n)). 10
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 25, 20, 27, 22, 19, 24, 23, 26, 21, 28, 29, 30, 49, 32, 45, 34, 35, 36, 31, 50, 33, 40, 37, 54, 41, 44, 81, 38, 43, 48, 125, 46, 75, 52, 47, 42, 121, 56, 63, 58, 77, 60, 53, 98, 39, 64, 55, 90, 59, 68, 135, 70, 61, 72, 169, 62, 51, 100, 67, 66, 175, 80, 99, 74, 71, 108, 343, 82, 105, 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) = A003961(a(A269380(2n+1))). a(n) = A250246(A269172(n)). a(n) = A005940(1+A269388(n)). Other identities. For all n >= 1: A001221(a(n)) = A302031(n). A001222(a(n)) = A302037(n). PROG (PARI) \\ With A269380 precomputed: A003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961 A302026(n) = if(1==n, n, if(!(n%2), 2*A302026(n/2), A003961(A302026(A269380(n))))); (Scheme, with memoization-macro definec) (definec (A302026 n) (cond ((= 1 n) n) ((even? n) (* 2 (A302026 (/ n 2)))) (else (A003961 (A302026 (A269380 n)))))) CROSSREFS Cf. A302025 (inverse permutation). Cf. A005940, A250246, A269172, A269388 (similar or related permutations). Cf. A003961, A064989, A269379, A269380, A302031, A302032, A302034, A302037. Sequence in context: A269396 A255408 A269172 * A285054 A090322 A076084 Adjacent sequences:  A302023 A302024 A302025 * A302027 A302028 A302029 KEYWORD nonn AUTHOR Antti Karttunen, Apr 03 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 9 11:08 EDT 2020. Contains 336323 sequences. (Running on oeis4.)