A106552 Semiprime + (smallest integer obtained by concatenating its two divisors).

26, 29, 42, 35, 41, 50, 58, 134, 80, 158, 146, 206, 92, 230, 172, 269, 126, 224, 170, 250, 287, 293, 200, 302, 311, 194, 323, 260, 329, 380, 228, 406, 341, 290, 359, 448, 350, 377, 296, 1232, 383, 464, 472, 330, 401, 488, 413, 1256, 440, 419, 470, 437, 512

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

First semiprime is 4; 4 is 2*2; 26=4+22.
Second semiprime is 6; 6 is 2*3 (23) or 3*2 (32); 29=6+23.
...
Eighth semiprime is 22; 22 is 2*11 (211) or 11*2 (112); 134=22+112.

Maple

count:= 0:
R:= NULL:
for n from 4 while count < 100 do
  F:= ifactors(n)[2];
  if nops(F) = 1 and F[1][2]=2 then count:= count+1; R:= R, n + F[1][1]*(1+10^(1+ilog10(F[1][1])))
  elif nops(F) = 2 and F[1][2]=1 and F[2][2]=1 then
     count:= count+1; p:= F[1][1]; q:= F[2][1];
     R:= R, n + min(p+10^(1+ilog10(p))*q, q+10^(1+ilog10(q))*p)
  fi
od:
R; # Robert Israel, Apr 08 2020

Mathematica

  cc[n_]:=Module[{fi=Transpose[FactorInteger[n]][[1]]}, If[Length[fi]==1, n+FromDigits[Flatten[ IntegerDigits/@{fi, fi}]], n+FromDigits[Flatten[ IntegerDigits/@SortBy[fi, First[IntegerDigits[#]]&]]]]]; cc/@ Select[ Range[300], PrimeOmega[#]==2&](* Harvey P. Dale, Dec 15 2013 *)

Prog

(PARI) lista(nn) = {for (n=1, nn, if (bigomega(n) == 2, f = factor(n); p = f[1, 1]; q = f[#f~, 1]; print1(n + min(p + q*10^(#Str(p)), q + p*10^(#Str(q))), ", "); ); ); } \\ Michel Marcus, Nov 25 2013

Crossrefs

Cf. A001358, A106553

Sequence in context: A081644 A256619 A055109 * A106550 A304949 A316617

Adjacent sequences: A106549 A106550 A106551 * A106553 A106554 A106555

Keyword

base,easy,nonn,look

Author

Eric Angelini, May 09 2005

Extensions

Corrected and extended by Harvey P. Dale, Dec 15 2013

a(32) corrected by Robert Israel, Apr 08 2020

Status

approved