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A093513 Transform of the prime sequence by the Rule89 cellular automaton. 10
1, 3, 4, 9, 10, 15, 16, 21, 22, 25, 26, 27, 28, 33, 34, 35, 36, 39, 40, 45, 46, 49, 50, 51, 52, 55, 56, 57, 58, 63, 64, 65, 66, 69, 70, 75, 76, 77, 78, 81, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 100, 105, 106, 111, 112, 115, 116, 117, 118, 119, 120, 121, 122, 123 (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..66.

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, A093514, A093515, A093516, A093517.

Sequence in context: A090120 A129783 A301919 * A047230 A277138 A327282

Adjacent sequences:  A093510 A093511 A093512 * A093514 A093515 A093516

KEYWORD

easy,nonn

AUTHOR

Ferenc Adorjan (fadorjan(AT)freemail.hu)

STATUS

approved

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Last modified January 23 22:16 EST 2020. Contains 331177 sequences. (Running on oeis4.)