A078816 Erroneous version of A081846.
6, 12, 19, 25, 33, 39, 46, 52, 60, 66, 72, 79, 85, 93, 99, 102, 112, 120, 126, 132, 139, 145, 153, 159, 166, 172, 180, 186, 192, 199, 205, 206, 219, 226, 232, 240, 246, 252, 259, 265, 273, 279, 286, 292, 300, 306, 313, 309, 326, 333, 339, 346, 352, 360, 366
Offset: 1
Keywords
Programs
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PARI
a(n)=vecmax(contfrac(sum(k=0,20,1/2^2^k)/n))
Formula
Conjecture : a(n) is asymptotic to c*n with 6
A384939 Maximum element in the continued fraction for (1/n) * Sum_{k>=0} 1/3^(2^k).
5, 11, 17, 24, 29, 35, 42, 48, 53, 60, 66, 72, 77, 84, 90, 96, 102, 108, 114, 121, 126, 132, 139, 145, 151, 156, 163, 169, 175, 181, 187, 193, 200, 205, 211, 218, 224, 229, 235, 242, 248, 253, 260, 266, 272, 279, 284, 290, 297, 303, 308, 314, 321, 327, 332, 339, 345, 351, 357, 363, 369, 375, 381, 387, 393, 400, 406, 411, 418, 424, 430, 436, 442, 448, 454, 460, 466, 472, 479, 484, 326, 497, 503, 508, 515, 521, 527, 532, 539, 545, 551, 558, 563, 569, 576, 582, 587, 594, 600, 606
Offset: 1
Keywords
Links
- Jeffrey O. Shallit, Simple continued fractions for some irrational numbers, J. Number Theory 11 (1979), no. 2, 209-217.
Programs
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Mathematica
m = 10; terms = 100; t1 = ConstantArray[0, 2*terms]; t2 = ConstantArray[1, 2*terms]; Until[t1 == t2, m++; PrintTemporary["m=",m]; s = Sum[1/3^(2^k), {k, 0, m}]; t1 = t2; t2 = Table[Max[ContinuedFraction[s/n]], {n, 1, 2*terms}]]; Take[t2, terms]