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A093516 Transform of the prime sequence by the Rule137 cellular automaton. 7
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 (list; graph; refs; listen; history; text; internal format)
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

Cf. A092855, A051006, A093510, A093511, A093512, A093513, A093514, A093515, A093517.

Sequence in context: A092827 A087904 A242203 * A246302 A278041 A063209

Adjacent sequences:  A093513 A093514 A093515 * A093517 A093518 A093519

KEYWORD

easy,nonn

AUTHOR

Ferenc Adorjan (fadorjan(AT)freemail.hu)

STATUS

approved

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Last modified December 8 12:55 EST 2016. Contains 278945 sequences.