A047473 - OEIS

A047473

Numbers that are congruent to {2, 3} mod 8.

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

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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

LINKS

Table of n, a(n) for n=1..59.

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

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.

Cf. A047467, A047468, A047470, A047471.

Sequence in context: A359251 A032804 A248407 * A270474 A008509 A281366

Adjacent sequences: A047470 A047471 A047472 * A047474 A047475 A047476

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vincenzo Librandi, Aug 06 2010

STATUS

approved