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A333300 Numbers that are of a form abab in some base (a <> b, a <> 0). 1
10, 30, 50, 60, 68, 70, 102, 119, 130, 136, 153, 182, 187, 204, 208, 221, 222, 234, 238, 260, 286, 296, 333, 338, 350, 364, 370, 390, 407, 416, 442, 444, 450, 481, 494, 500, 520, 546, 550, 555, 572, 592, 598, 600, 629, 650, 666, 700, 703, 715, 738, 740, 750 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The first terms with 2, 3, ..., 6 representations are 520, 4930, 117130, 111270100, and 3142012250. - Giovanni Resta, Mar 15 2020

LINKS

Richárd Pintér, Table of n, a(n) for n = 1..10000

Richárd Pintér, Haskell source

EXAMPLE

10 = 1010_2 is a term, 30 = 1010_3 and 50 = 1212_3 also.

MATHEMATICA

bxy[n_] := Block[{x, y, b, s, bb = Select[Sqrt[ Divisors[n] - 1], IntegerQ[#] && # > 1 && (1 + #^2) # <= n && #^4-#^2-2 >= n &]}, Flatten[ Table[s = Solve[(1 + b^2) (b x + y) == n && 0<x<b && 0<=y<b && x!=y, {x, y}, Integers]; If[s == {}, {}, {b, x, y} /. s], {b, bb}], 1]]; Select[ Range@ 750, bxy[#] != {} &] (* Giovanni Resta, Mar 14 2020 *)

CROSSREFS

Sequence in context: A104863 A326122 A027183 * A096844 A031299 A124164

Adjacent sequences:  A333297 A333298 A333299 * A333301 A333302 A333303

KEYWORD

nonn,base

AUTHOR

Richárd Pintér, Mar 14 2020

STATUS

approved

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Last modified September 30 02:48 EDT 2020. Contains 337432 sequences. (Running on oeis4.)