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Revision History for A302026

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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)).
(history; published version)

#12 by Susanna Cuyler at Fri Apr 06 10:15:22 EDT 2018

STATUS

proposed

approved

#11 by Antti Karttunen at Fri Apr 06 05:40:45 EDT 2018

STATUS

editing

proposed

#10 by Antti Karttunen at Wed Apr 04 12:39:02 EDT 2018

COMMENTS

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

#9 by Antti Karttunen at Wed Apr 04 12:35:05 EDT 2018

NAME

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

#8 by Antti Karttunen at Wed Apr 04 05:20:35 EDT 2018

LINKS

Antti Karttunen, <a href="/A302026/b302026.txt">Table of n, a(n) for n = 1..10000</a>

#7 by Antti Karttunen at Tue Apr 03 11:06:02 EDT 2018

DATA

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, 38, 50, 33, 40, 37, 42, 54, 41, 44, 81, 46, 38, 43, 48, 125, 50, 46, 75, 52, 47, 54, 42, 121, 56, 63, 58, 77, 60, 53, 62, 98, 39, 64, 55, 66, 90, 59, 68, 135, 70, 61, 72, 169, 74, 62, 51, 76, 100, 67, 78, 66, 175, 80, 99, 82, 74, 71, 84, 108, 343, 86, 82, 105, 88

#6 by Antti Karttunen at Tue Apr 03 10:59:18 EDT 2018

PROG

A302026(n) = if(1==n, n, if(!(n%2), 2*A302026(n/2), A003961(A302026(A269380(n)))));

#5 by Antti Karttunen at Tue Apr 03 09:44:15 EDT 2018

PROG

(Scheme, with memoization-macro definec)

(definec (A302026 n) (cond ((= 1 n) n) ((even? n) (* 2 (A302026 (/ n 2)))) (else (A003961 (A302026 (A269380 n))))))

#4 by Antti Karttunen at Tue Apr 03 08:37:45 EDT 2018

FORMULA

Other identities. For all n >= 1:

A001221(a(n)) = A302031(n).

A001222(a(n)) = A302037(n).

CROSSREFS

Cf. A003961, A064989, A269379, A269380, A302031, A302032, A302034, A302037.

#3 by Antti Karttunen at Tue Apr 03 08:33:34 EDT 2018

NAME

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

FORMULA

a(1) = 1, a(2n) = 2*a(n), a(2n+1) = A003961(A302026a(A269380(a2n2n+1))).

a(n) = A250246(A269172(n)).

a(n) = A005940(1+A269388(n)).

CROSSREFS

Cf. A005940, A250246, A269172, A269388 (similar or related permutations).