The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A078971 Numbers n such that C(4n,n)/(3n+1) (A002293) is not divisible by 4. 25
 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 (list; graph; refs; listen; history; text; internal format)
 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

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

Last modified May 12 11:55 EDT 2021. Contains 343821 sequences. (Running on oeis4.)