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A154470
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Rewriting function for Wolfram's e[x_][y_] -> x[x[y]] symbolic system transformation, implemented on nihilistic S-expressions (parenthesizations) encoded by A014486.
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2
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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
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OFFSET
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0,3
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COMMENTS
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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.
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..2055
S. Wolfram, A New Kind of Science, Wolfram Media Inc., (2002), pp. 102--104, 896-898.
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PROG
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(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))))))
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CROSSREFS
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Differs from A001477 for the first time at n=29, where a(n)=32.
Sequence in context: A246099 A280865 A124231 * A194907 A090106 A167662
Adjacent sequences: A154467 A154468 A154469 * A154471 A154472 A154473
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, Jan 11 2009
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STATUS
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approved
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