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A046397 Palindromes which are the product of exactly 7 distinct primes.

%I A046397 #16 Jun 17 2024 15:38:09
%S A046397 22444422,24266242,26588562,35888853,36399363,43777734,47199174,
%T A046397 51066015,53588535,53888835,55233255,59911995,60066006,62588526,
%U A046397 62700726,62888826,81699618,87788778,89433498,122434221,202040202
%N A046397 Palindromes which are the product of exactly 7 distinct primes.
%C A046397 The original name "Palindromes with exactly 7 distinct prime factors" did not exclude that one or more of the factors occurred to a higher power: this is sequence A373467. As the listed data show, terms of this sequence must be squarefree. - _M. F. Hasler_, Jun 06 2024
%H A046397 Robert Israel, <a href="/A046397/b046397.txt">Table of n, a(n) for n = 1..10000</a>
%e A046397 The first two palindromes with 7 distinct prime factors are 20522502 = 2 * 3^2 * 7 * 11 * 13 * 17 * 67 and 21033012 = 2^2 * 3 * 7 * 11 * 13 * 17 * 103, but these are excluded since one of the prime factors occurs to a higher power.
%e A046397 a(1) = 22444422 = 2 * 3 * 7 * 11 * 13 * 37 * 101, which is squarefree, is therefore the first term of this sequence.
%p A046397 digrev:= proc(n) local L,i;
%p A046397   L:= convert(n,base,10);
%p A046397   add(L[-i]*10^(i-1),i=1..nops(L))
%p A046397 end proc:
%p A046397 filter:= proc(n) local F;
%p A046397   F:= ifactors(n)[2];
%p A046397   nops(F) = 7 and map(t -> t[2],F)=[1$7]
%p A046397 end proc:
%p A046397 Res:= NULL:
%p A046397 count:= 0:
%p A046397 for d from 2  while count < 100 do
%p A046397   if d::even then
%p A046397     m:= d/2;
%p A046397     for n from 10^(m-1) to 10^m-1 while count < 100 do
%p A046397       v:= n*10^m+digrev(n);
%p A046397       if filter(v) then count:= count+1; Res:= Res, v; fi;
%p A046397     od;
%p A046397   else
%p A046397     m:= (d-1)/2;
%p A046397     for n from 10^(m-1) to 10^m-1 while count < 100 do
%p A046397       for y from 0 to 9 while count < 100 do
%p A046397          v:= n*10^(m+1)+y*10^m+digrev(n);
%p A046397          if filter(v) then count:= count+1; Res:= Res, v; fi;
%p A046397     od od
%p A046397   fi
%p A046397 od:
%p A046397 Res; # _Robert Israel_, Jan 20 2020
%o A046397 (PARI) A046397_upto(N, start=vecprod(primes(7)), num_fact=7)={ my(L=List()); is_A002113(start)&& start--; while(N >= start = nxt_A002113(start), omega(start)==num_fact && issquarefree(start) && listput(L, start)); L} \\ _M. F. Hasler_, Jun 06 2024
%Y A046397 Cf. A046333 (similar but prime factors counted with multiplicity), A373467 (similar but counting just the distinct prime divisors).
%Y A046397 Cf. A002113 (palindromes), A123321 (products of 7 distinct primes), A176655 (numbers with omega = 7 distinct prime divisors).
%K A046397 nonn,base
%O A046397 1,1
%A A046397 _Patrick De Geest_, Jun 15 1998