A047589 Numbers that are congruent to {6, 7} mod 8.

6, 7, 14, 15, 22, 23, 30, 31, 38, 39, 46, 47, 54, 55, 62, 63, 70, 71, 78, 79, 86, 87, 94, 95, 102, 103, 110, 111, 118, 119, 126, 127, 134, 135, 142, 143, 150, 151, 158, 159, 166, 167, 174, 175, 182, 183, 190, 191, 198, 199, 206, 207, 214, 215, 222, 223, 230, 231

Offset

1,1

Comments

These are the values of n for which binomial(n,6) is odd. See Maple code. - Gary Detlefs, Nov 29 2011

Links

Table of n, a(n) for n=1..58.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = 8*n-a(n-1)-3 with n>1, a(1)=6. - Vincenzo Librandi, Aug 06 2010

a(n) = 6*floor((n-1)/2) + n + 5. - Gary Detlefs, Nov 29 2011

a(n) = a(n-1)+a(n-2)-a(n-3). G.f.: x*(6+x+x^2)/((1-x)^2*(1+x)). - Colin Barker, Mar 18 2012

a(n) = (1-3*(-1)^n+8*n)/2. - Colin Barker, May 14 2012

Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2)*Pi/16 - log(2)/8 - sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 18 2021

Maple

for i from 1 to 240 do if(floor((i mod 8)/6) <>0) then print(i) fi od; # Gary Detlefs, Nov 30 2011

Mathematica

LinearRecurrence[{1, 1, -1}, {6, 7, 14}, 60] (* Harvey P. Dale, Sep 11 2017 *)

Crossrefs

Union of A017137 and A004771.

Cf. A047451, A047521.

Sequence in context: A283772 A080402 A146308 * A125996 A315836 A315837

Adjacent sequences: A047586 A047587 A047588 * A047590 A047591 A047592

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved