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A183298
Complement of A147875.
1
1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85
OFFSET
1,2
FORMULA
(See the Mathematica code.)
a(n) = n+floor(sqrt(2n/5)) if 2n > floor(sqrt(2n/5))(5*floor(sqrt(2n/5))+1) and a(n) = n+floor(sqrt(2n/5))-1 otherwise. - Chai Wah Wu, Oct 12 2024
MATHEMATICA
a=5/2; b=3/2;
F[n_]:=a*n^2+b*n;
R[n_]:=(n/a+((b-1)/(2a))^2)^(1/2);
G[n_]:=n-1+Ceiling[R[n]-(b-1)/(2a)];
Table[F[n], {n, 60}]
Table[G[n], {n, 100}]
PROG
(Python)
from math import isqrt
def A183298(n): return n+(m:=isqrt((k:=n<<1)//5))-(k<=m*(5*m+1)) # Chai Wah Wu, Oct 12 2024
CROSSREFS
Cf. A147875.
Sequence in context: A089590 A052406 A022306 * A081023 A165332 A031179
KEYWORD
nonn
AUTHOR
Clark Kimberling, Jan 03 2011
STATUS
approved