A107129 Numbers n which are palindromic in more bases b, 1<b<n, than any previous number.

1, 3, 5, 10, 21, 36, 60, 80, 120, 180, 252, 300, 720, 1080, 1440, 1680, 2160, 2520, 3600, 5040, 7560, 9240, 10080, 12600, 15120, 18480, 25200, 27720, 36960, 41580, 45360, 50400, 55440, 83160, 110880, 131040, 166320, 221760, 277200, 332640, 360360

Offset

0,2

Comments

Records by number in A037183, by indices in A065531.

Except for 3, 5 and 21 they are all even and except for the first seven, they are all multiples of twelve.

References

Michael Trott, The Mathematica GuideBook for Programming, Springer, 2004, page 218.

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..91

Example

1 has no palindromic representation in bases 2 to n.
3 = 11_2.
5 = 101_2, 11_4.
10 = 101_3, 22_4, 11_9.
21 = 10101_2, 111_4, 33_6, 11_20.
36960 = 5775_19, 3(90)3_97, (176)(176)_209, (168)(168)_219,
(165)(165)_223, (160)(160)_230, (154)(154)_239, (140)(140)_263, (132)(132)_279,
(120)(120)_307, (112)(112)_329, (110)(110)_335, (105)(105)_351, (96)(96)_384,
(88)(88)_419, (84)(84)_439, (80)(80)_461, (77)(77)_479, (70)(70)_527,
(66)(66)_559, (60)(60)_615, (56)(56)_659, (55)(55)_671, (48)(48)_769,
(44)(44)_839, (42)(42)_879, (40)(40)_923, (35)(35)_1055, (33)(33)_1119,
(32)(32)_1154, (30)(30)_1231, (28)(28)_1319, (24)(24)_1539, (22)(22)_1679,
(21)(21)_1759, (20)(20)_1847, (16)(16)_2309, (15)(15)_2463, (14)(14)_2639,
(12)(12)_3079, (11)(11)_3359, (10)(10)_3695, 88_4619, 77_5279, 66_6159, 55_7391,
44_9239, 33_12319, 22_18479, 11_36959.

Mathematica

f[n_] := Block[{s = Floor@ Sqrt[n + 1] - 1, b = 2, c = If[IntegerQ@ Sqrt[n + 1], -2, -1]}, While[b < s + 2, idn = IntegerDigits[n, b]; If[ idn == Reverse@ idn, c++]; b++]; c + Count[ Mod[n, Range@ s], 0]]; f[n_] := 0 /; n < 3;
k = 0; mx = -1; lst = {}; While[ k < 360000001, c = f@ k; If[ c > mx, AppendTo[lst, k]; mx = c]; k++]; lst

Crossrefs

Cf. A037183, A065531, A106801, A135549.

Sequence in context: A018104 A134365 A076862 * A037183 A214209 A024424

Adjacent sequences: A107126 A107127 A107128 * A107130 A107131 A107132

Keyword

nonn,base

Author

Michael Trott (mtrott(AT)wolfram.com) and Robert G. Wilson v, May 12 2005

Status

approved