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%I #20 Feb 18 2023 08:09:36
%S 13,12,132,1518,15015,204204,10444434,241879638,20340535215,
%T 242194868916,136969856585562,2400532020354468,484576809394483806,
%U 200939345091539746692
%N Least non-palindromic number k such that k and its digital reversal both have exactly n prime divisors.
%C This sequence does not allow ending in 0, else a(8) = 208888680, a(11) = 64635504163230 and a(13) = 477566276048801940. - _Michael S. Branicky_, Feb 14 2023
%F a(n) >= A239696(n). - _Daniel Suteu_, Feb 18 2023
%e a(1)=13=13 since 31=31,
%e a(2)=12=2^2*3 since 21=3*7,
%e a(3)=132=2^2*3*11 since 231=3*7*11,
%e ...
%e a(7)=10444434=2*3*7*11*13*37*47 since 43444401=3*7*11*13*17*23*37,
%e a(8)=241879638=2*3*7*11*13*17*23*103 since 836978142=2*3*7*11*13*23*73*83.
%t r[n_] := FromDigits[ Reverse[ IntegerDigits[ n]]]; f[n_] := Block[{k = r[n], len = Length[ FactorInteger[n]]}, If[k != n && len == Length[ FactorInteger[ r[n]]], len, 0]]; t = Table[0, {10}]; Do[ a = f[n]; If[a > 0 && t[[a]] == 0, t[[a]] = n; Print[{a, n}]], {n, 107}]; t
%o (PARI)
%o generate(A, B, n) = A=max(A, vecprod(primes(n))); (f(m, p, j) = my(list=List()); forprime(q=p, sqrtnint(B\m, j), if(q==5 && m%2==0, next); my(v=m*q); while(v <= B, if(j==1, my(r=fromdigits(Vecrev(digits(v)))); if(v>=A && r != v && omega(r) == n, listput(list, v)), if(v*(q+1) <= B, list=concat(list, f(v, q+1, j-1)))); v *= q)); list); vecsort(Vec(f(1, 2, n)));
%o a(n) = my(x=vecprod(primes(n)), y=2*x); while(1, my(v=generate(x, y, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ _Daniel Suteu_, Feb 18 2023
%Y Cf. A110843, A110819, A239696.
%K base,hard,nonn
%O 1,1
%A _Ryan Propper_ and _Robert G. Wilson v_, Sep 21 2005
%E Edited and extended by _Giovanni Resta_, Jan 16 2006
%E a(9)-a(10) from _Giovanni Resta_, Feb 23 2014
%E a(11)-a(13) from _Michael S. Branicky_, Feb 14 2023
%E a(14) from _Daniel Suteu_, Feb 18 2023
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