A154470 Rewriting function for Wolfram's e[x_][y_] -> x[x[y]] symbolic system transformation, implemented on nihilistic S-expressions (parenthesizations) encoded by A014486.

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

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

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.

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

Adjacent sequences: A154467 A154468 A154469 * A154471 A154472 A154473

Keyword

nonn

Author

Antti Karttunen, Jan 11 2009

Status

approved