A003153 a(n) = integer nearest n*(1+sqrt(2)). (Formerly M1331)

2, 5, 7, 10, 12, 14, 17, 19, 22, 24, 27, 29, 31, 34, 36, 39, 41, 43, 46, 48, 51, 53, 56, 58, 60, 63, 65, 68, 70, 72, 75, 77, 80, 82, 84, 87, 89, 92, 94, 97, 99, 101, 104, 106, 109, 111, 113, 116, 118, 121, 123, 126, 128, 130, 133, 135, 138, 140, 142, 145

Offset

1,1

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

L. Carlitz, R. Scoville and V. E. Hoggatt, Jr., Pellian representatives, Fibonacci Quarterly, 10, issue 5, 1972, 449-488.

Mathematica

ni[n_]:=Module[{c=1+Sqrt[2], a, b, x}, x=c n; a=Floor[x]; b=Ceiling[x]; If[x-a<b-x, a, b]]; Array[ni, 60] (* Harvey P. Dale, May 04 2011 *)
Table[Round[n*(1 + Sqrt[2])], {n, 1, 100}] (* G. C. Greubel, Aug 16 2018 *)

Prog

(PARI) a(n) = round(n*(1+sqrt(2))); \\ Michel Marcus, Sep 07 2017
(Magma) [Round(n*(1+Sqrt(2))): n in [1..100]]; // G. C. Greubel, Aug 16 2018

Crossrefs

Sequence in context: A195437 A081032 A082845 * A187475 A274285 A022849

Adjacent sequences: A003150 A003151 A003152 * A003154 A003155 A003156

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Better description 1/97.

Status

approved