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A260184
Numbers n written in base 10 that are palindromic in exactly three bases b, 2 <= b <= 10 and not simultaneously bases 2, 4 and 8.
1
9, 10, 21, 40, 55, 80, 85, 100, 130, 154, 164, 178, 191, 203, 235, 242, 255, 257, 273, 282, 292, 300, 328, 400, 455, 585, 656, 819, 910, 2709, 6643, 8200, 14762, 32152, 53235, 74647, 428585, 532900, 1181729, 1405397, 4210945, 5259525, 27711772, 719848917, 43253138565
OFFSET
1,1
FORMULA
The intersection of A006995, A014190, A014192, A029952, A029953, A029954, A029803, A029955 & A002113 which yields just three members, not simultaneously bases 2, 4 and 8.
EXAMPLE
273 is in the sequence because 100010001_2 = 101010_3 = 10101_4 = 2043_5 = 1133_6 = 540_7 = 421_8 = 333_9 = 273_10 and three of the bases, namely 2, 4 & 9, yield palindromes.
MATHEMATICA
(* see A214425 and set all terms as lst, then *)
gQ[n_] := Count[ palQ[n, #] & /@ {2, 4, 8}, True];
Select[ lst, gQ[#] != 3 &]
CROSSREFS
Sequence in context: A102238 A104646 A214425 * A109463 A326523 A061410
KEYWORD
nonn,base
AUTHOR
STATUS
approved