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A274773
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a(n) = floor(sqrt(2*n-1) + 1/2) - abs(2*(n-1) - (floor(sqrt(2*n-1) + 1/2))^2) + 1.
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1
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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
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OFFSET
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1,3
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COMMENTS
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All terms are odd.
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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Table[Floor[Sqrt[2 n - 1] + 1/2] - Abs[2 (n - 1) - Floor[Sqrt[2 n - 1] + 1/2]^2] + 1, {n, 1, 120}]
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PROG
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(Python)
from gmpy2 import isqrt_rem
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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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