cp's OEIS Frontend

A093510 Transform of the prime sequence by the Rule30 cellular automaton.

%I A093510 #4 Feb 16 2025 08:32:53
%S A093510 2,3,6,8,9,11,12,14,15,17,18,20,21,23,24,25,29,30,32,33,37,38,39,41,
%T A093510 42,44,45,47,48,49,53,54,55,59,60,62,63,67,68,69,71,72,74,75,79,80,81,
%U A093510 83,84,85,89,90,91,97,98,99,101,102,104,105,107,108,110,111,113,114,115
%N A093510 Transform of the prime sequence by the Rule30 cellular automaton.
%C A093510 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 A093510 Ferenc Adorjan, <a href="http://web.axelero.hu/fadorjan/aronsf.pdf">Binary mapping of monotonic sequences - the Aronson and the CA functions</a>
%H A093510 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ElementaryCellularAutomaton.html">Elementary Cellular Automaton</a>
%H A093510 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule30 Elementary Cellular Automaton</a>
%o A093510 (PARI) {ca_tr(ca,v)= /* Calculates the Cellular Automaton transform of the vector v by the rule ca */
%o A093510 local(cav=vector(8),a,r=[],i,j,k,l,po,p=vector(3));
%o A093510 a=binary(min(255,ca));k=matsize(a)[2];forstep(i=k,1,- 1,cav[k-i+1]=a[i]);
%o A093510 j=0;l=matsize(v)[2];k=v[l];po=1;
%o A093510 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 A093510 return(r) /* See the function "isin" at A092875 */}
%Y A093510 Cf. A092855, A051006, A093511, A093512, A093513, A093514, A093515, A093516, A093517.
%K A093510 easy,nonn
%O A093510 1,1
%A A093510 Ferenc Adorjan (fadorjan(AT)freemail.hu)