%I #3 Jun 29 2008 03:00:00
%S 1,3,10,16,22,26,27,28,34,35,36,40,46,50,51,52,56,57,58,64,65,66,70,
%T 76,77,78,82,86,87,88,92,93,94,95,96,100,106,112,116,117,118,119,120,
%U 121,122,123,124,125,126,130,134,135,136,142,143,144,145,146,147,148,154
%N Transform of the prime sequence by the Rule137 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, A093513, A093514, A093515, A093517.
%K easy,nonn
%O 1,2
%A Ferenc Adorjan (fadorjan(AT)freemail.hu)