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.

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

Links

Table of n, a(n) for n=1..45.

Rick Regan, Finding numbers that are palindromic in multiple bases

Index entries for sequences related to palindromes

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

Cf. A214426, A214425.

Sequence in context: A102238 A104646 A214425 * A109463 A326523 A061410

Adjacent sequences: A260181 A260182 A260183 * A260185 A260186 A260187

Keyword

nonn,base

Author

Giovanni Resta and Robert G. Wilson v, Jul 17 2015

Status

approved