A003153 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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