|
%I #26 Oct 30 2021 13:42:08
%S 10,30,50,60,68,70,102,119,130,136,153,182,187,204,208,221,222,234,
%T 238,260,286,296,333,338,350,364,370,390,407,416,442,444,450,481,494,
%U 500,520,546,550,555,572,592,598,600,629,650,666,700,703,715,738,740,750
%N Numbers that are of the form abab in some base (a <> b, a <> 0).
%C The first terms with 2, 3, ..., 6 representations are 520, 4930, 117130, 111270100, and 3142012250. - _Giovanni Resta_, Mar 15 2020
%H Richárd Pintér, <a href="/A333300/b333300.txt">Table of n, a(n) for n = 1..10000</a>
%H Richárd Pintér, <a href="/A333300/a333300.hs.txt">Haskell source</a>
%e 10 = 1010_2 is a term, 30 = 1010_3 and 50 = 1212_3 also.
%t 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 *)
%o (Python)
%o def ok(n):
%o base = 2
%o while True:
%o base3, base2 = base**3, base**2
%o if base3 + base > n: return False
%o for a in range(1, base):
%o for b in range(base):
%o if a == b: continue
%o t = a*(base3 + base) + b*(base2 + 1)
%o if t == n: return True
%o elif t > n: break
%o base += 1
%o print([k for k in range(751) if ok(k)]) # _Michael S. Branicky_, Oct 30 2021
%K nonn,base
%O 1,1
%A _Richárd Pintér_, Mar 14 2020
|
