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A293523
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Persistently squarefree numbers for base-3 shifting: Numbers n such that all terms in finite set of positive numbers [n, floor(n/3), floor(n/9), floor(n/27), ..., floor(n/3^k)>0] are squarefree.
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2
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1, 2, 3, 5, 6, 7, 10, 11, 15, 17, 19, 21, 22, 23, 30, 31, 33, 34, 35, 46, 47, 51, 53, 57, 58, 59, 65, 66, 67, 69, 70, 71, 91, 93, 94, 95, 101, 102, 103, 105, 106, 107, 138, 139, 141, 142, 143, 154, 155, 159, 161, 173, 174, 177, 178, 179, 195, 197, 199, 201, 202, 203, 209, 210, 211, 213, 214, 215, 273, 274, 281, 282
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OFFSET
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1,2
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COMMENTS
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If there is any number present which itself is not divisible by 3 (is in A001651), then 3n is also present in this sequence.
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LINKS
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PROG
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(PARI)
\\ A naivish algorithm:
allocatemem(2^30);
up_to_level = 10;
up_to = (3^(1+up_to_level))-1;
vekkuli = vector(up_to);
vekkuli[1] = 1;
vekkuli[2] = -1;
write("b293523.txt", 1, " ", 1);
write("b293523.txt", 2, " ", 2);
kA293523 = 3; for(n=3, up_to, vekkuli[n] = moebius(n)*vekkuli[n\3]; if(vekkuli[n], write("b293523.txt", kA293523, " ", n); kA293523++; ));
(PARI)
is_persistently_squarefree(n, base) = { while(n>1, if(!issquarefree(n), return(0)); n \= base); (1); };
isA293523(n) = is_persistently_squarefree(n, 3);
n=0; k=1; while(k <= 10000, n=n+1; if(isA293523(n), write("b293523.txt", k, " ", n); k=k+1));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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