A154470 - OEIS

%I #4 Mar 31 2012 13:21:18

%S 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,

%T 26,27,28,32,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,

%U 49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,74

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

%C 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.

%H A. Karttunen, <a href="/A154470/b154470.txt">Table of n, a(n) for n = 0..2055</a>

%H S. Wolfram, <a href="http://www.wolframscience.com/nksonline/page-102">A New Kind of Science, Wolfram Media Inc., (2002), pp. 102</a>--104, 896-898.

%o (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))))))

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

%K nonn

%O 0,3

%A _Antti Karttunen_, Jan 11 2009