OFFSET
1,1
COMMENTS
Also n for which A006906(n) is even, or equivalently n for which A000009(n) is even (since A006906 and A000009 have the same parity).
The number of partitions of a(n) into distinct parts with an even number of parts equals the number of such partitions with an odd number of parts: A067661(a(n)) = A067659(a(n)). See, e.g., the Freitag-Busam reference, p. 410 given in A036499. - Wolfdieter Lang, Jan 19 2016
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
FORMULA
A010815(a(n)) = A067661(a(n)) - A067659(a(n)) = 0, n >= 1. See a comment above. - Wolfdieter Lang, Jan 19 2016
MATHEMATICA
Complement[Range[200], Select[Accumulate[Range[0, 200]]/3, IntegerQ]] (* G. C. Greubel, Jun 06 2017 *)
PROG
(Python)
from math import isqrt
def A090864(n):
def f(x): return n+(m:=isqrt(24*x+1)+1)//6+(m-2)//6
kmin, kmax = 0, 1
while f(kmax) > kmax:
kmax <<= 1
while kmax-kmin > 1:
kmid = kmax+kmin>>1
if f(kmid) <= kmid:
kmax = kmid
else:
kmin = kmid
return kmax # Chai Wah Wu, Aug 29 2024
(PARI) a(n) = my(q, r); [q, r]=divrem(sqrtint(24*n), 3); n + q + (r >= bitnegimply(1, q)); \\ Kevin Ryde, Sep 15 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jon Perry, Feb 12 2004
EXTENSIONS
More terms from Reinhard Zumkeller, Apr 22 2006
Edited by Ray Chandler, Dec 14 2011
Edited by Jon E. Schoenfield, Nov 25 2016
STATUS
approved