

A093514


Transform of the prime sequence by the Rule90 cellular automaton.


7



2, 3, 4, 9, 11, 15, 17, 21, 23, 25, 29, 33, 37, 39, 41, 45, 47, 49, 53, 55, 59, 63, 67, 69, 71, 75, 79, 81, 83, 85, 89, 91, 97, 99, 101, 105, 107, 111, 113, 115, 127, 129, 131, 133, 137, 141, 149, 153, 157, 159, 163, 165, 167, 169, 173, 175, 179, 183, 191, 195, 197, 201
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OFFSET

1,1


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.
n is in this sequence if either n2 OR n is prime but not both. Similar simple propositional rules can be given for all "RuleXXX" transforms of primes (or any strictly monotone sequence with a welldefined characteristic function) because the idea in these sequences is to take the characteristic function, consider it as an infinite binary word, apply one generation of some onedimensional cellular automaton rule "XXX" to it and define the new sequence by this characteristic function.  Antti Karttunen, Apr 22 2004
For example, 2 is included because 0 is not prime, but 2 is. 3 is included because 1 is not prime, but 3 is. 4 is included because 2 is prime, although 4 is not. 5 is not included because both 3 and 5 are primes, 9 is included because 7 is prime, but 9 is not.


LINKS

Table of n, a(n) for n=1..62.
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[ki+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, A093515, A093516, A093517.
Characteristic function for this sequence is A010051(n2) + A010051(n) (modulo 2). Naturally none of the terms of A006512 occur here.
Sequence in context: A118223 A212989 A211546 * A215810 A080231 A217493
Adjacent sequences: A093511 A093512 A093513 * A093515 A093516 A093517


KEYWORD

easy,nonn


AUTHOR

Ferenc Adorjan (fadorjan(AT)freemail.hu)


STATUS

approved



