A080718 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.

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

Offset

1,2

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..145

Example

1255 = 5*251, 12955 = 5*2591, 17482 = 2*8741, 100255 = 5*20051, 146137=317*461, etc.

Maple

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:
A080718:= select(filter, [1, seq(4+9*i, i=1..10^6)]); # Robert Israel, May 04 2014

Mathematica

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 *)

Crossrefs

The following sequences are all closely related: A020342, A014575, A080718, A280928, A048936, A144563.

Sequence in context: A067203 A230544 A280928 * A219993 A237562 A304829

Adjacent sequences: A080715 A080716 A080717 * A080719 A080720 A080721

Keyword

nonn,base

Author

Jeff Heleen, Mar 06 2003

Extensions

Edited by N. J. A. Sloane, Jan 03 2009

Incorrect entry 163797 removed by Robert Israel, May 04 2014

Status

approved