login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A268304 Odd numbers n such that binomial(6*n, 2*n) == -1 (mod 8). 1
1, 5, 21, 73, 85, 273, 293, 297, 329, 341, 529, 545, 1041, 1057, 1089, 1093, 1105, 1173, 1189, 1193, 1297, 1317, 1321, 1353, 1365, 2065, 2081, 2113, 2117, 2129, 2177, 2181, 2209, 2577, 2593, 4113, 4129, 4161, 4165, 4177, 4225, 4229, 4257, 4353, 4357, 4373, 4417, 4421, 4433 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The primes p of this sequence are those that give the even semiprimes of A268303.
LINKS
Marc Chamberland and Karl Dilcher, A Binomial Sum Related to Wolstenholme's Theorem, J. Number Theory, Vol. 171, Issue 11 (Nov. 2009), pp. 2659-2672. See Table 2 p. 2669.
MATHEMATICA
Select[Range[1, 5000, 2], Mod[Binomial[6 #, 2 #], 8] == 7 &] (* Michael De Vlieger, Feb 07 2016 *)
PROG
(PARI) isok(n) = (n%2) && Mod(binomial(6*n, 2*n), 8) == Mod(-1, 8);
(Python)
from __future__ import division
A268304_list, b, m1, m2 = [], 15, [21941965946880, -54854914867200, 49244258396160, -19011472727040, 2933960577120, -126898662960, 771887070, 385943535, 385945560], [10569646080, -25763512320, 22419210240, -8309145600, 1209116160, -46992960, 415800, 311850, 311850]
for n in range(10**3):
if b % 8 == 7:
A268304_list.append(2*n+1)
b = b*m1[-1]//m2[-1]
for i in range(8):
m1[i+1] += m1[i]
m2[i+1] += m2[i] # Chai Wah Wu, Feb 05 2016
CROSSREFS
Sequence in context: A202462 A354701 A055280 * A273450 A186948 A271251
KEYWORD
nonn
AUTHOR
Michel Marcus, Jan 31 2016
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)