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A080718
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1, together with numbers n that are the product of two primes p and q such that the multiset of the digits of n coincides with the multiset of the digits of p and q.
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7
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1, 1255, 12955, 17482, 25105, 100255, 101299, 105295, 107329, 117067, 124483, 127417, 129595, 132565, 145273, 146137, 149782, 174082, 174298, 174793, 174982, 250105, 256315, 263155, 295105, 297463, 307183, 325615, 371893, 536539
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OFFSET
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1,2
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COMMENTS
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Except for 1, this sequence is a subsequence of A280928. More specifically, members of A280928 are also members of this sequence if and only if they are semiprime. - Ely Golden, Jan 11 2017
This sequence has no equivalent in odd bases. This is because any equivalent of A280928 in an odd base must have all terms having at least 3 prime factors. - Ely Golden, Jan 11 2017
All entries other than 1 are congruent to 4 mod 9, because p*q == p + q mod 9 (with p and q not both divisible by 3) implies p*q == 4 mod 9. - Robert Israel, May 05 2014
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LINKS
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EXAMPLE
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1255 = 5*251, 12955 = 5*2591, 17482 = 2*8741, 100255 = 5*20051, 146137=317*461, etc.
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MAPLE
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filter:= proc(n) local F, p, q, Ln, Lpq;
F:= ifactors(n)[2];
if nops(F) > 2 or convert(F, `+`)[2]<>2 then return false fi;
p:= F[1][1];
if nops(F) = 2 then q:= F[2][1] else q:= F[1][1] fi;
Ln:= sort(convert(n, base, 10));
Lpq:= sort([op(convert(p, base, 10)), op(convert(q, base, 10))]);
evalb(Ln = Lpq);
end proc:
filter(1):= true:
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MATHEMATICA
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ptpQ[n_]:=Module[{sidn=Sort[IntegerDigits[n]], fi=Transpose[ FactorInteger[ n]]}, fi[[2]]=={1, 1}&&Sort[Flatten[ IntegerDigits/@ fi[[1]]]]==sidn]; Join[{1}, Select[Range[4, 550000, 9], ptpQ]] (* Harvey P. Dale, Jun 22 2014 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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