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.

111, 414, 777, 35853, 1226221, 7673767, 7744477, 9396939, 859767958, 11211911211, 12467976421, 72709290727, 93969696939, 1030507050301, 1120237320211, 1225559555221, 1234469644321, 1334459544331, 3254595954523, 10048622684001, 100330272033001, 100827848728001

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Example

111 = 37*3
414 = 23*3*3*2
777 = 37*7*3
35853 = 37*19*17*3
1226221 = 1201*1021
7673767 = 79111*97
7744477 = 3119*191*13
9396939 = 31013*101*3
859767958 = 2731*199*113*7*2

Mathematica

(* generate palindromes with even n *)
poli[n_Integer?EvenQ]:=FromDigits[Join[#, Reverse[#]]]&/@
DeleteCases[Tuples[Range[0, 9], n/2], {0.., ___}]
(* generate palindromes with odd n *)
poli[n_Integer?OddQ]:=Flatten[Table[FromDigits[Join[#, {k}, Reverse[#]]]&/@
DeleteCases[Tuples[Range[0, 9], (n-1)/2], {0.., ___}], {k, 0, 9}]]
(* find descending factor sequence *)
descendFACTOR[n_Integer]:=
PalindromeQ[StringJoin[Reverse[ToString/@Flatten[Table[#1, #2]&@@@#]]]]&&
Length[#]>1&@FactorInteger[n]
(* example for palindromes of size 7 *)
Parallelize@Select[poli[7], descendFACTOR]//Sort//AbsoluteTiming

Crossrefs

Similar to A364050. Subsequence of A002113 and A024619.

Sequence in context: A225329 A277960 A304831 * A304516 A259246 A205830

Adjacent sequences: A364020 A364021 A364022 * A364024 A364025 A364026

Keyword

nonn,base,hard

Author

Vitaliy Kaurov, Jul 04 2023

Status

approved