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A047390 Numbers that are congruent to {0, 3, 5} mod 7. 1
0, 3, 5, 7, 10, 12, 14, 17, 19, 21, 24, 26, 28, 31, 33, 35, 38, 40, 42, 45, 47, 49, 52, 54, 56, 59, 61, 63, 66, 68, 70, 73, 75, 77, 80, 82, 84, 87, 89, 91, 94, 96, 98, 101, 103, 105, 108, 110, 112, 115, 117, 119, 122, 124, 126, 129, 131, 133, 136, 138, 140, 143 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also numbers k such that k*(k+2)*(k+4) is divisible by 7. - Bruno Berselli, Dec 28 2017

LINKS

Table of n, a(n) for n=1..62.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

FORMULA

a(n) = 2*n + floor(n/3) + (n^2 mod 3), with offset 0, a(0)=0. - Gary Detlefs, Mar 19 2010

From Bruno Berselli, Mar 29 2011: (Start)

G.f.: x^2*(3 + 2*x + 2*x^2)/((1 - x)^2*(1 + x + x^2)).

a(n) = (1/3)*(7*n - 6 - A049347(n-1)) = A047391(n) - A079978(n-1). (End)

a(n) = n + ceiling(4*(n-1)/3) - 1. - Arkadiusz Wesolowski, Sep 18 2012

a(n) = 2*(n-1) + ceiling((n-1)/3). - Karl V. Keller, Jr., Nov 01 2014

From Wesley Ivan Hurt, Jun 10 2016: (Start)

a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.

a(n) = 7*n/3 - 2 - 2*sin(2*n*Pi/3)/(3*sqrt(3)).

a(3*k) = 7*k-2, a(3*k-1) = 7*k-4, a(3*k-2) = 7*k-7. (End)

MAPLE

seq(2*n+floor(n/3)+(n^2 mod 3), n=0..52); # Gary Detlefs, Mar 19 2010

MATHEMATICA

Select[Range[0, 150], MemberQ[{0, 3, 5}, Mod[#, 7]]&] (* Harvey P. Dale, Dec 07 2011 *)

CoefficientList[Series[x (3 + 2 x + 2 x^2)/((1 - x)^2 (1 + x + x^2)), {x, 0, 70}], x] (* Vincenzo Librandi, Nov 02 2014 *)

PROG

(MAGMA) [n: n in [0..122] | n mod 7 in [0, 3, 5]];  // Bruno Berselli, Mar 29 2011

(Python)

import math

a = lambda n: 2*(n-1)+math.ceil((n-1)/3.0)

for n in range(1, 101): print(a(n), end = ", ") # Karl V. Keller, Jr., Nov 01 2014

(PARI) is(n)=!!setsearch([0, 3, 5], n%7) \\ Charles R Greathouse IV, Nov 09 2014

(PARI) a(n)=(7*n-5)\3 \\ Charles R Greathouse IV, Nov 09 2014

CROSSREFS

Cf. A011655, A047391, A049347, A079978.

Sequence in context: A190511 A260466 A033035 * A184653 A263085 A206334

Adjacent sequences:  A047387 A047388 A047389 * A047391 A047392 A047393

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 25 16:17 EDT 2019. Contains 326324 sequences. (Running on oeis4.)