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A003152 A Beatty sequence: a(n) = floor(n*(1+1/sqrt(2))).
(Formerly M2392)
26
1, 3, 5, 6, 8, 10, 11, 13, 15, 17, 18, 20, 22, 23, 25, 27, 29, 30, 32, 34, 35, 37, 39, 40, 42, 44, 46, 47, 49, 51, 52, 54, 56, 58, 59, 61, 63, 64, 66, 68, 69, 71, 73, 75, 76, 78, 80, 81, 83, 85, 87, 88, 90, 92, 93, 95, 97, 99, 100, 102, 104, 105, 107, 109, 110, 112, 114, 116 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Numbers with an even number of trailing 0's in their minimal representation in terms of the positive Pell numbers (A317204). - Amiram Eldar, Mar 16 2022
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
L. Carlitz, R. Scoville, and V. E. Hoggatt, Jr. Pellian representations, Fibonacci Quarterly, Vol. 10, No. 5 (1972), pp. 449-488.
Joshua N. Cooper and Alexander W. N. Riasanovsky, On the Reciprocal of the Binary Generating Function for the Sum of Divisors, J. Int. Seq., Vol. 16 (2013), Article 13.1.8; preprint, 2012.
N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence).
MAPLE
Digits := 100: t := evalf(1+sin(Pi/4)): A:= n->floor(t*n): seq(floor((t*n)), n=1..68); # Zerinvary Lajos, Mar 27 2009
MATHEMATICA
Table[Floor[n (1 + 1/Sqrt[2])], {n, 70}] (* Vincenzo Librandi, Dec 26 2015 *)
PROG
(Magma) [Floor(n*(1+1/Sqrt(2))): n in [1..70]]; // Vincenzo Librandi, Dec 26 2015
(PARI) a(n)=n+sqrtint(2*n^2)\2 \\ Charles R Greathouse IV, Jan 25 2022
CROSSREFS
Complement of A003151.
The following sequences are all essentially the same, in the sense that they are simple transformations of each other, with A003151 as the parent: A003151, A001951, A001952, A003152, A006337, A080763, A082844 (conjectured), A097509, A159684, A188037, A245219 (conjectured), A276862. - N. J. A. Sloane, Mar 09 2021
Bisections: A001952, A001954.
Sequence in context: A329833 A059541 A189682 * A325913 A283965 A193599
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 02:55 EDT 2024. Contains 370952 sequences. (Running on oeis4.)