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A274773 a(n) = floor(sqrt(2*n-1) + 1/2) - abs(2*(n-1) - (floor(sqrt(2*n-1) + 1/2))^2) + 1. 1
1, 1, 3, 1, 3, 3, 1, 3, 5, 3, 1, 3, 5, 5, 3, 1, 3, 5, 7, 5, 3, 1, 3, 5, 7, 7, 5, 3, 1, 3, 5, 7, 9, 7, 5, 3, 1, 3, 5, 7, 9, 9, 7, 5, 3, 1, 3, 5, 7, 9, 11, 9, 7, 5, 3, 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1, 3, 5, 7, 9, 11, 13, 11, 9, 7, 5, 3, 1, 3, 5, 7, 9, 11, 13, 13, 11, 9, 7, 5, 3, 1, 3, 5, 7, 9, 11, 13, 15, 13, 11, 9, 7, 5, 3, 1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11, 9, 7, 5, 3 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

First bisection of A004738.

All terms are odd.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Ilya Gutkovskiy, Illustrations

Eric Weisstein's World of Mathematics, Smarandache Sequences

EXAMPLE

Triangle begins:

  1;

  1, 3;

  1, 3, 3;

  1, 3, 5, 3;

  1, 3, 5, 5, 3;

  1, 3, 5, 7, 5, 3;

  1, 3, 5, 7, 7, 5, 3;

  1, 3, 5, 7, 9, 7, 5, 3;

  1, 3, 5, 7, 9, 9, 7, 5, 3;

  ...

Read like the Ulam spiral, starting with 1:

    x  7  x  5  x  3  x  1

    7  x  5  x  3  x  1  x

    x  5  x  3  x  1  x  3

    5  x  3  x  1  x  3  x

    x  3  x  1  x  3  x  5

    3  x  1  x  3  x  5  x

    x  1  x  3  x  5  x  7

    1  x  3  x  5  x  7  x

MATHEMATICA

Table[Floor[Sqrt[2 n - 1] + 1/2] - Abs[2 (n - 1) - Floor[Sqrt[2 n - 1] + 1/2]^2] + 1, {n, 1, 120}]

PROG

from gmpy2 import isqrt_rem

def A274773(n):

    i, j = isqrt_rem(2*n-1)

    return int(i+2 - abs(j-2*(i+1)) if 4*(i-j) + 1 <= 0 else i+1 - abs(j-1)) # Chai Wah Wu, Aug 15 2016

CROSSREFS

Cf. A004738, A005408.

Sequence in context: A216637 A234308 A050141 * A132752 A131241 A133599

Adjacent sequences:  A274770 A274771 A274772 * A274774 A274775 A274776

KEYWORD

nonn,easy,tabl

AUTHOR

Ilya Gutkovskiy, Aug 11 2016

STATUS

approved

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Last modified September 24 03:26 EDT 2021. Contains 347623 sequences. (Running on oeis4.)