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Search: id:A093510
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| A093510 |
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Transform of the prime sequence by the Rule30 cellular automaton. |
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+0
8
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| 2, 3, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 25, 29, 30, 32, 33, 37, 38, 39, 41, 42, 44, 45, 47, 48, 49, 53, 54, 55, 59, 60, 62, 63, 67, 68, 69, 71, 72, 74, 75, 79, 80, 81, 83, 84, 85, 89, 90, 91, 97, 98, 99, 101, 102, 104, 105, 107, 108, 110, 111, 113, 114, 115
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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.
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LINKS
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Ferenc Adorjan, Binary mapping of monotonic sequences - the Aronson and the CA functions
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Eric Weisstein's World of Mathematics, Rule30 Elementary Cellular Automaton
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PROGRAM
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(PARI) {ca_tr(ca, v)= /* Calculates the Cellular Automaton transform of the vector v by the rule ca */
local(cav=vector(8), a, r=[], i, j, k, l, po, p=vector(3));
a=binary(min(255, ca)); k=matsize(a)[2]; forstep(i=k, 1, - 1, cav[k-i+1]=a[i]);
j=0; l=matsize(v)[2]; k=v[l]; po=1;
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)));
return(r) /* See the function "isin" at A092875 */}
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CROSSREFS
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Cf. A092855, A051006, A093511, A093512, A093513, A093514, A093515, A093516, A093517.
Sequence in context: A047405 A084090 A047286 this_sequence A013948 A013952 A105042
Adjacent sequences: A093507 A093508 A093509 this_sequence A093511 A093512 A093513
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KEYWORD
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easy,nonn
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AUTHOR
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Ferenc Adorjan (fadorjan(AT)freemail.hu)
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