A107129 Numbers n which are palindromic in more bases b, 1

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

Author

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

Keywords

• nonn
• base

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.

Examples

			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.
		

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

Crossrefs

Cf. A037183, A065531, A106801, A135549.

Programs

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