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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Union of A017137 and A004771.

Cf. A047451, A047521.

Programs

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 *)

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