A239307 - OEIS

%I #10 Jul 16 2026 12:08:39

%S 4,6,9,22,26,33,39,55,62,77,93,121,143,169,187,202,226,262,303,339,

%T 341,393,505,622,626,707,781,933,939,961,1111,1177,1243,1313,1441,

%U 1469,1661,1717,1991,2042,2062,2066,2206,2402,2426,2446,2462,2602,2642,3063,3093

%N Semiprimes n = p*q such that reverse(n)=reverse(p)*reverse(q) where reverse(n) is also semiprime.

%C Subsequence of A001358.

%H Giovanni Resta, <a href="/A239307/b239307.txt">Table of n, a(n) for n = 1..10000</a>

%e 1469 = 13*113 is in the sequence because reverse(1469)=reverse(13)*reverse(113) => 9641 = 31*311 where 31 and 311 are prime numbers.

%p with(numtheory):lst:={}:T1:=array(1..300):T2:=array(1..300):k:=0:

%p    for n from 1 to 1000 do:

%p        p:=ithprime(n):xp:=convert(p,base,10):

%p        np:=nops(xp):sp:=sum('xp[np-i+1]*10^(i-1)','i'=1..np):

%p          if type(sp,prime)=true

%p          then

%p          k:=k+1:T1[k]:=p:T2[k]:=sp:

%p          else

%p          fi:

%p     od:

%p          for i from 1 to k do:

%p            for j from i to k do:

%p               x:=T1[i]*T1[j]:y:=convert(x,base,10):n2:=nops(y):

%p               s:=sum('y[n2-i+1]*10^(i-1)', 'i'=1..n2):

%p               if T2[i]*T2[j]=s

%p               then

%p               lst:=lst union {x}:

%p               else

%p               fi:

%p           od:

%p         od:

%p         print(lst):

%t spQ[n_]:=Module[{f=FactorInteger[n][[;;,1]],f1,f2,rn},If[Length[f]==1,f=Flatten[{f,f}]];f1=f[[1]];f2=f[[2]];rn=IntegerReverse[n];PrimeOmega[rn] == 2 && rn==IntegerReverse[f1]IntegerReverse[f2]]; Select[Range[3100],PrimeOmega[#]==2&&spQ[#]&] (* _Harvey P. Dale_, Jul 16 2026 *)

%Y Cf. A007500, A001358.

%K nonn,base,changed

%O 1,1

%A _Michel Lagneau_, Mar 15 2014