|
|
A197878
|
|
a(n) = floor(2*(1 + sqrt(2))*n).
|
|
3
|
|
|
4, 9, 14, 19, 24, 28, 33, 38, 43, 48, 53, 57, 62, 67, 72, 77, 82, 86, 91, 96, 101, 106, 111, 115, 120, 125, 130, 135, 140, 144, 149, 154, 159, 164, 168, 173, 178, 183, 188, 193, 197, 202, 207, 212, 217, 222, 226, 231, 236, 241, 246, 251, 255, 260, 265, 270
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
First differences are 4 and 5. Also, there is no immediate pattern in parity of a(n).
Answer: I would not call the sequences A086843, A086844, A196468 'similar' to (a(n)). The first differences d =5,5,5,5,4,5,5,5,5,4,... are a Sturmian sequence (d(n)) with slope alpha = 2 + sqrt(8) and intercept 0. We give d offset 0 by setting d(0):=4. By Hofstadter's Fundamental Theorem of eta-sequences, the chunks 45555 and 455555 occur following a Sturmian sequence with density beta = (sqrt(8) - 2)/(3 - sqrt(8)). Since beta = 2 + sqrt(8) = alpha, the sequence (d(n)) is fixed point of the substitution 4->45555, 5->455555. See A197879 for a complete description of the parity pattern of (a(n)). - Michel Dekking, Jan 24 2017
|
|
LINKS
|
D. R. Hofstadter, Eta-Lore [Cached copy, with permission]
|
|
FORMULA
|
|
|
MATHEMATICA
|
Table[Floor[((2+Sqrt[8]))*n], {n, 100}]
|
|
PROG
|
(Magma) [Floor(2*(1 + Sqrt(2))*n): n in [1..100]]; // G. C. Greubel, Aug 18 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|