

A047529


Numbers that are congruent to {1, 3, 7} mod 8.


2



1, 3, 7, 9, 11, 15, 17, 19, 23, 25, 27, 31, 33, 35, 39, 41, 43, 47, 49, 51, 55, 57, 59, 63, 65, 67, 71, 73, 75, 79, 81, 83, 87, 89, 91, 95, 97, 99, 103, 105, 107, 111, 113, 115, 119, 121, 123, 127, 129, 131, 135, 137, 139, 143, 145, 147, 151, 153, 155, 159
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OFFSET

1,2


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).


FORMULA

a(n) = (24*n+2*sqrt(3)*sin(2*Pi*n/3)+6*cos(2*Pi*n/3)15)/9.  Fred Daniel Kline, Nov 12 2015
From Colin Barker, Nov 12 2015: (Start)
a(n) = a(n1) + a(n3)  a(n4) for n>4.
G.f.: x*(x^3+4*x^2+2*x+1) / ((x1)^2*(x^2+x+1)). (End)
a(n+3) = a(n) + 8 for all n in Z.  Michael Somos, Nov 15 2015
a(3k) = 8k1, a(3k1) = 8k5, a(3k2) = 8k7.  Wesley Ivan Hurt, Jun 13 2016
a(n) = 8 * floor((n1) / 3) + 2^(((n1) mod 3) + 1)  1.  Fred Daniel Kline, Aug 09 2016


EXAMPLE

G.f. = x + 3*x^2 + 7*x^3 + 9*x^4 + 11*x^5 + 15*x^6 + 17*x^7 + 19*x^8 + 23*x^9 + ...


MAPLE

A047529:=n>(24*n+2*sqrt(3)*sin(2*Pi*n/3)+6*cos(2*Pi*n/3)15)/9: seq(A047529(n), n=1..100); # Wesley Ivan Hurt, Jun 13 2016


MATHEMATICA

Select[Range[150], MemberQ[{1, 3, 7}, Mod[#, 8]]&] (* Harvey P. Dale, May 02 2011 *)
LinearRecurrence[{1, 0, 1, 1}, {1, 3, 7, 9}, 100] (* Vincenzo Librandi, Jun 14 2016 *)


PROG

(PARI) Vec(x*(x^3+4*x^2+2*x+1)/((x1)^2*(x^2+x+1)) + O(x^100)) \\ Colin Barker, Nov 12 2015
(PARI) {a(n) = n\3 * 8 + [1, 1, 3][n%3 + 1]}; /* Michael Somos, Nov 15 2015 */
(MAGMA) [n : n in [0..150]  n mod 8 in [1, 3, 7]]; // Wesley Ivan Hurt, Jun 13 2016


CROSSREFS

Sequence in context: A027897 A027892 A158938 * A125667 A072939 A171947
Adjacent sequences: A047526 A047527 A047528 * A047530 A047531 A047532


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



