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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)