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A364023 Palindromes that have at least two distinct prime factors and whose prime factors, listed (with multiplicity) in descending order and concatenated, form a palindrome in base 10.

%I A364023 #36 Aug 05 2023 21:42:52
%S A364023 111,414,777,35853,1226221,7673767,7744477,9396939,859767958,
%T A364023 11211911211,12467976421,72709290727,93969696939,1030507050301,
%U A364023 1120237320211,1225559555221,1234469644321,1334459544331,3254595954523,10048622684001,100330272033001,100827848728001
%N A364023 Palindromes that have at least two distinct prime factors and whose prime factors, listed (with multiplicity) in descending order and concatenated, form a palindrome in base 10.
%e A364023 111 = 37*3
%e A364023 414 = 23*3*3*2
%e A364023 777 = 37*7*3
%e A364023 35853 = 37*19*17*3
%e A364023 1226221 = 1201*1021
%e A364023 7673767 = 79111*97
%e A364023 7744477 = 3119*191*13
%e A364023 9396939 = 31013*101*3
%e A364023 859767958 = 2731*199*113*7*2
%t A364023 (* generate palindromes with even n *)
%t A364023 poli[n_Integer?EvenQ]:=FromDigits[Join[#,Reverse[#]]]&/@
%t A364023 DeleteCases[Tuples[Range[0,9],n/2],{0..,___}]
%t A364023 (* generate palindromes with odd n *)
%t A364023 poli[n_Integer?OddQ]:=Flatten[Table[FromDigits[Join[#,{k},Reverse[#]]]&/@
%t A364023 DeleteCases[Tuples[Range[0,9],(n-1)/2],{0..,___}],{k,0,9}]]
%t A364023 (* find descending factor sequence *)
%t A364023 descendFACTOR[n_Integer]:=
%t A364023 PalindromeQ[StringJoin[Reverse[ToString/@Flatten[Table[#1,#2]&@@@#]]]]&&
%t A364023 Length[#]>1&@FactorInteger[n]
%t A364023 (* example for palindromes of size 7 *)
%t A364023 Parallelize@Select[poli[7],descendFACTOR]//Sort//AbsoluteTiming
%Y A364023 Similar to A364050. Subsequence of A002113 and A024619.
%K A364023 nonn,base,hard
%O A364023 1,1
%A A364023 _Vitaliy Kaurov_, Jul 04 2023