A078971 Numbers n such that C(4n,n)/(3n+1) (A002293) is not divisible by 4.

0, 1, 3, 5, 11, 13, 21, 43, 45, 53, 85, 171, 173, 181, 213, 341, 683, 685, 693, 725, 853, 1365, 2731, 2733, 2741, 2773, 2901, 3413, 5461, 10923, 10925, 10933, 10965, 11093, 11605, 13653, 21845, 43691, 43693, 43701, 43733, 43861, 44373, 46421, 54613

Offset

1,3

Comments

Stanica observes that the sequence in binary forms a pattern where 1 bits are inserted into the word 1010101...:

1 11

101 1011 1101

10101 101011 101101 110101

1010101 10101011 10101101 10110101 11010101...

Links

Chai Wah Wu, Table of n, a(n) for n = 1..5050

P. Stanica, p^q Catalan numbers and squarefree binomial coefficients, arXiv:math/0010148 [math.NT], 2000.

Mathematica

Select[ Range[0, 65000], Mod[ Binomial[4#, # ]/(3# + 1), 4] != 0 &] (* Robert G. Wilson v, Oct 12 2005 *)

Prog

(PARI) isok(n) = binomial(4*n, n)/(3*n+1) % 4; \\ Michel Marcus, Apr 16 2015
(Magma) [n: n in [0..2*10^4] | not IsZero(Binomial(4*n, n) div (3*n+1) mod 4)]; // Vincenzo Librandi, Apr 16 2015
(Python)
from __future__ import division
A078971_list = []
for t in range(100):
    A078971_list.append((2**(2*t)-1)//3)
    for j in range(t):
        A078971_list.append((2**(2*t+1)+2**(2*j+1)-1)//3) # Chai Wah Wu, Mar 06 2016

Crossrefs

Cf. A000225 (C(2n, n)/(n+1) is not divisible by 2), A003462 (C(3n, n)/(2n+1) is not divisible by 3), A003463 (C(5n, n)/(4n+1) is not divisible by 5).

Sequence in context: A207325 A295243 A179017 * A266723 A129096 A079448

Adjacent sequences: A078968 A078969 A078970 * A078972 A078973 A078974

Keyword

nonn

Author

Benoit Cloitre, Jan 14 2003

Extensions

Comments and more terms from Ralf Stephan, Oct 30 2003

a(28)-a(44) from Robert G. Wilson v, Oct 12 2005

Status

approved