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%I #3 Jun 29 2008 03:00:00
%S 1,3,4,9,10,15,16,21,22,25,26,27,28,33,34,35,36,39,40,45,46,49,50,51,
%T 52,55,56,57,58,63,64,65,66,69,70,75,76,77,78,81,82,85,86,87,88,91,92,
%U 93,94,95,96,99,100,105,106,111,112,115,116,117,118,119,120,121,122,123
%N Transform of the prime sequence by the Rule89 cellular automaton.
%C As described in A051006, a monotonic sequence can be mapped into a fractional real. Then the binary digits of that real can be treated (transformed) by an elementary cellular automaton. Taken resulted sequence of binary digits as a fractional real, it can be mapped back into a sequence, as in A092855.
%H Ferenc Adorjan, <a href="http://web.axelero.hu/fadorjan/aronsf.pdf">Binary mapping of monotonic sequences - the Aronson and the CA functions</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%o (PARI) {ca_tr(ca,v)= /* Calculates the Cellular Automaton transform of the vector v by the rule ca */
%o local(cav=vector(8),a,r=[],i,j,k,l,po,p=vector(3));
%o a=binary(min(255,ca));k=matsize(a)[2];forstep(i=k,1,- 1,cav[k-i+1]=a[i]);
%o j=0;l=matsize(v)[2];k=v[l];po=1;
%o for(i=1,k+2,j*=2;po=isin(i,v,l,po);j=(j+max(0,sign(po)))% 8;if(cav[j+1],r=concat(r,i)));
%o return(r) /* See the function "isin" at A092875 */}
%Y Cf. A092855, A051006, A093510, A093511, A093512, A093514, A093515, A093516, A093517.
%K easy,nonn
%O 1,2
%A Ferenc Adorjan (fadorjan(AT)freemail.hu)
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