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A183294
Complement of A005449.
1
1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87
OFFSET
1,2
FORMULA
(See the Mathematica code.)
a(n) = n + A180447(n-1). - Kevin Ryde, Sep 01 2024
a(n) = n+m+1 if 2n>=m(3m+5)+4 and a(n) = n+m otherwise where m = floor(sqrt(2n/3)). - Chai Wah Wu, Nov 04 2024
MATHEMATICA
a=3/2; b=1/2;
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
(PARI) a(n) = n + (sqrtint(24*n)+1)\6; \\ Kevin Ryde, Sep 01 2024
(Python)
from math import isqrt
def A183294(n): return n+(m:=isqrt((k:=n<<1)//3))+(k>=m*(3*m+5)+4) # Chai Wah Wu, Nov 04 2024
CROSSREFS
Sequence in context: A377721 A216846 A288674 * A039234 A025020 A028974
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 03 2011
STATUS
approved