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A046332 Palindromes with exactly 6 prime factors (counted with multiplicity).

%I A046332 #22 Jun 07 2024 08:05:19
%S A046332 2772,2992,6776,8008,21112,21712,21912,23632,23832,25452,25752,25952,
%T A046332 27472,28782,29392,40104,40304,40404,42024,42924,44044,44144,44744,
%U A046332 44944,45954,46764,46864,48984,53235,54945,55755,59895,60606,61216
%N A046332 Palindromes with exactly 6 prime factors (counted with multiplicity).
%H A046332 Chai Wah Wu, <a href="/A046332/b046332.txt">Table of n, a(n) for n = 1..5000</a>
%F A046332 Intersection of A002113 and A046306. - _M. F. Hasler_, Jun 06 2024
%p A046332 N:= 6: # to get all terms of up to N digits
%p A046332 digrev:= proc(n) local L,Ln; L:= convert(n,base,10);Ln:= nops(L);
%p A046332 add(L[i]*10^(Ln-i),i=1..Ln);
%p A046332 end proc:
%p A046332 Res:= NULL:
%p A046332 for d from 2 to N do
%p A046332   if d::even then
%p A046332     m:= d/2;
%p A046332     Res:= Res, select(numtheory:-bigomega=6,
%p A046332            [seq](n*10^m + digrev(n), n=10^(m-1)..10^m-1));
%p A046332   else
%p A046332     m:= (d-1)/2;
%p A046332     Res:= Res, select(numtheory:-bigomega=6,
%p A046332            [seq](seq(n*10^(m+1)+y*10^m+digrev(n), y=0..9), n=10^(m-1)..10^m-1));
%p A046332   fi
%p A046332 od:
%p A046332 map(op,[Res]); # _Robert Israel_, Dec 23 2014
%o A046332 (Python)
%o A046332 from sympy import factorint
%o A046332 def palQgen10(l): # generator of palindromes in base 10 of length <= 2*l
%o A046332     if l > 0:
%o A046332         yield 0
%o A046332         for x in range(1,l+1):
%o A046332             for y in range(10**(x-1),10**x):
%o A046332                 s = str(y)
%o A046332                 yield int(s+s[-2::-1])
%o A046332             for y in range(10**(x-1),10**x):
%o A046332                 s = str(y)
%o A046332                 yield int(s+s[::-1])
%o A046332 A046332_list = [x for x in palQgen10(4) if sum(list(factorint(x).values())) == 6]
%o A046332 # _Chai Wah Wu_, Dec 21 2014
%o A046332 (PARI) A046332_upto(N, start=1, num_fact=6)={ my(L=List()); while(N >= start = nxt_A002113(start), bigomega(start)==num_fact && listput(L, start)); L} \\ _M. F. Hasler_, Jun 06 2024
%Y A046332 Cf. A002113 (palindromes), A046306 (bigomega = 6), A046319.
%Y A046332 Cf. A046396 (similar but terms must be squarefree), A373466 (similar, but only distinct prime divisors are counted).
%K A046332 nonn,base
%O A046332 1,1
%A A046332 _Patrick De Geest_, Jun 15 1998