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A063957 Numbers not of the form round(m*sqrt(2)) for any integer m, i.e., complement of A022846. 6
2, 5, 9, 12, 15, 19, 22, 26, 29, 32, 36, 39, 43, 46, 50, 53, 56, 60, 63, 67, 70, 73, 77, 80, 84, 87, 90, 94, 97, 101, 104, 108, 111, 114, 118, 121, 125, 128, 131, 135, 138, 142, 145, 149, 152, 155, 159, 162, 166, 169, 172, 176, 179, 183, 186, 189, 193, 196, 200 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Similar to Beatty sequences: where a pair of complementary Beatty sequences are floor(n*c) and floor(n*c/(c-1)) for c an irrational constant > 1, these pairs of complementary sequences are in general round(n*c) and round((n-1/2)*c/(c-1)) for c an irrational constant > 1.

REFERENCES

Clark Kimberling, BEATTY SEQUENCES AND TRIGONOMETRIC FUNCTIONS, Integers 16 (2016), #A15.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = round((n - 1/2)*(2 + sqrt(2))) = round(n*3.4142...-1.7071...).

EXAMPLE

round(m*sqrt(2)) starts 1,3,4,6,7,8,10,11,13,... so this sequence must start 2,5,9,12,...

PROG

(PARI) { f=2 + sqrt(2); t=f/2; for (n=1, 1000, write("b063957.txt", n, " ", round(n*f - t)) ) } \\ Harry J. Smith, Sep 03 2009

CROSSREFS

Cf. A001951, A001952, A007064, A022846. Consider natural numbers A000027 as a triangle 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc., then the a(n) indicate rows without a square.

Sequence in context: A279171 A297465 A108165 * A184579 A186274 A184926

Adjacent sequences:  A063954 A063955 A063956 * A063958 A063959 A063960

KEYWORD

nonn

AUTHOR

Henry Bottomley, Sep 04 2001

STATUS

approved

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Last modified March 26 23:02 EDT 2019. Contains 321565 sequences. (Running on oeis4.)