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
(Python)
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
KEYWORD
AUTHOR
Ilya Gutkovskiy, Aug 11 2016
STATUS
approved