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

Author

Antti Karttunen, Jan 11 2009

Keywords

• nonn

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

• Antti Karttunen, Table of n, a(n) for n = 0..2055
• Stephen Wolfram, A New Kind of Science, Wolfram Media Inc., (2002), pp. 102--104, 896-898.

Crossrefs

Cf. A014486.

Differs from A001477 for the first time at n=29, where a(n)=32.

Programs

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))))))