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A047473
Numbers that are congruent to {2, 3} mod 8.
0
2, 3, 10, 11, 18, 19, 26, 27, 34, 35, 42, 43, 50, 51, 58, 59, 66, 67, 74, 75, 82, 83, 90, 91, 98, 99, 106, 107, 114, 115, 122, 123, 130, 131, 138, 139, 146, 147, 154, 155, 162, 163, 170, 171, 178, 179, 186, 187, 194, 195, 202, 203, 210, 211, 218, 219, 226, 227, 234
OFFSET
1,1
COMMENTS
Numbers k such that k and k+2 have the same digital binary sum. - Benoit Cloitre, Dec 01 2002
Also, numbers k such that k*(3*k + 1)/8 + 1/4 is a nonnegative integer. - Bruno Berselli, Feb 14 2017
FORMULA
a(n) = 8*n - a(n-1) - 11 for n>1, a(1)=2. - Vincenzo Librandi, Aug 06 2010
From R. J. Mathar, Oct 08 2011: (Start)
a(n) = 4*n - 7/2 - 3*(-1)^n/2.
G.f.: x*(2 + x + 5*x^2)/((1 + x)*(1 - x)^2). (End)
a(1)=2, a(2)=3, a(3)=10; for n>3, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Sep 28 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = (2-sqrt(2))*Pi/16 + sqrt(2)*log(sqrt(2)+1)/8 - log(2)/8. - Amiram Eldar, Dec 18 2021
MATHEMATICA
Flatten[# + {2, 3} &/@ (8 Range[0, 30])] (* or *) LinearRecurrence[{1, 1, -1}, {2, 3, 10}, 60] (* Harvey P. Dale, Sep 28 2012 *)
CROSSREFS
Union of A017089 and A017101.
Sequence in context: A359251 A032804 A248407 * A270474 A008509 A281366
KEYWORD
nonn,easy
EXTENSIONS
More terms from Vincenzo Librandi, Aug 06 2010
STATUS
approved