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 A254109 If n <= 63, a(n) = n; for n > 63: a(32n + 14) = 8*n + 5, a(64n + 30) = 4*n + 3, and for other cases with n > 63: a(2n) = 2*a(n), a(2n+1) = 2*a(n) + 1. 3
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 21, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 7 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This sequence is a rewriting-recurrence which attempts to contract the perimeter of binary boundary coded holeless polyhexes and other fusenes by 2 or 4 edges, where first possible (from the least significant end of n), and if no such contraction is possible, then it fixes n. Together with recurrence A258009 can be used to obtain the terms of A258012, please see comments there. LINKS Antti Karttunen, Table of n, a(n) for n = 0..8191 FORMULA If n <= 63, a(n) = n; for n > 63: a(32n + 14) = 8*n + 5, a(64n + 30) = 4*n + 3, and for other cases with n > 63: a(2n) = 2*a(n), a(2n+1) = 2*a(n) + 1. EXAMPLE The first term where a(n) is different from n occurs at n=78, as 78 = "1001110" in binary, where the clause a(32n + 14) = 8*n + 5 will rewrite the trailing "01110" part as "101", resulting binary string "10101" = 21 in decimal. PROG (Scheme, two variants, the first one utilizing a memoizing definec-macro) (definec (A254109 n) (cond ((<= n 63) n) ((= 14 (modulo n 32)) (+ 5 (* 8 (floor->exact (/ n 32))))) ((= 30 (modulo n 64)) (+ 3 (* 4 (floor->exact (/ n 64))))) (else (+ (modulo n 2) (* 2 (A254109 (floor->exact (/ n 2)))))))) ;; Faster, iterative version: (define (A254109 n) (let loop ((n n) (s 0) (p2 1)) (cond ((<= n 63) (+ (* p2 n) s)) ((= 14 (modulo n 32)) (+ (* p2 8 (floor->exact (/ n 32))) s (* p2 5))) ((= 30 (modulo n 64)) (+ (* p2 4 (floor->exact (/ n 64))) s (* p2 3))) ((even? n) (loop (/ n 2) s (+ p2 p2))) (else (loop (/ (- n 1) 2) (+ s p2) (+ p2 p2)))))) CROSSREFS Cf. A255561, A255568, A258009, A258012. Sequence in context: A000027 A001477 A087156 * A317945 A292579 A262530 Adjacent sequences:  A254106 A254107 A254108 * A254110 A254111 A254112 KEYWORD nonn,base AUTHOR Antti Karttunen, Mar 11 2015 EXTENSIONS Recurrence corrected to match the intended usage by Antti Karttunen, Jun 05 2015 STATUS approved

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Last modified April 15 08:18 EDT 2021. Contains 342977 sequences. (Running on oeis4.)