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A154470 Rewriting function for Wolfram's e[x_][y_] -> x[x[y]] symbolic system transformation, implemented on nihilistic S-expressions (parenthesizations) encoded by A014486. 2
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, 32, 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, 74 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Here we use the empty list () as a marker for symbol 'e'. Any sublist like (... ()(x1 x2 ... xn)(y1 y2 ... yn) ...) is transformed into the form (... x1 x2 ... xn (x1 x2 ... xn (y1 y2 ... yn)) ...). A054471 gives the iterations of this function, starting from initial value 31706.
LINKS
PROG
(Scheme:) (define (*A154470 s) (cond ((null? s) s) ((and (null? (car s)) (>= (length s) 3) (pair? (second s)) (pair? (third s))) (append (second s) (cons (append (second s) (list (third s))) (*A154470 (cdddr s))))) (else (cons (*A154470 (car s)) (*A154470 (cdr s))))))
CROSSREFS
Differs from A001477 for the first time at n=29, where a(n)=32.
Sequence in context: A280865 A124231 A352800 * A194907 A090106 A369464
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 11 2009
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)