A093516 - OEIS

A093516

Transform of the prime sequence by the Rule137 cellular automaton.

1, 3, 10, 16, 22, 26, 27, 28, 34, 35, 36, 40, 46, 50, 51, 52, 56, 57, 58, 64, 65, 66, 70, 76, 77, 78, 82, 86, 87, 88, 92, 93, 94, 95, 96, 100, 106, 112, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 130, 134, 135, 136, 142, 143, 144, 145, 146, 147, 148, 154

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OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..61.

Ferenc Adorjan, Binary mapping of monotonic sequences - the Aronson and the CA functions

Eric Weisstein's World of Mathematics, Elementary Cellular Automaton

PROG

(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 */}

CROSSREFS