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

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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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.

Programs

Magma

[Round(n*(1+Sqrt(2))): n in [1..100]]; // G. C. Greubel, Aug 16 2018

Mathematica

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

PARI

a(n) = round(n*(1+sqrt(2))); \\ Michel Marcus, Sep 07 2017

Extensions

Better description 1/97.