A329975 Beatty sequence for 1 + x + x^2, where x is the real solution of 1/x + 1/(1+x+x^2) = 1.
4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 53, 57, 61, 65, 69, 73, 77, 81, 85, 89, 93, 97, 101, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 155, 159, 163, 167, 171, 175, 179, 183, 187, 191, 195, 199, 203, 208, 212, 216, 220, 224, 228, 232
Offset: 1
Links
- Eric Weisstein's World of Mathematics, Beatty Sequence.
- Index entries for sequences related to Beatty sequences
Programs
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Mathematica
Solve[1/x + 1/(1 + x + x^2) == 1, x] u = 1/3 (27/2 - (3 Sqrt[69])/2)^(1/3) + (1/2 (9 + Sqrt[69]))^(1/3)/3^(2/3); u1 = N[u, 150] RealDigits[u1, 10][[1]] (* A060006 *) Table[Floor[n*u], {n, 1, 50}] (* A329974 *) Table[Floor[n*(1 + u + u^2)], {n, 1, 50}] (* A329975 *) Plot[1/x + 1/(1 + x + x^2) - 1, {x, -2, 2}]
Formula
a(n) = floor(n*(1+x+x^2)), where x = 1.324717... is the constant in A060006.
Comments