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A047373 Numbers that are congruent to {0, 1, 2, 3, 5} mod 7. 1
0, 1, 2, 3, 5, 7, 8, 9, 10, 12, 14, 15, 16, 17, 19, 21, 22, 23, 24, 26, 28, 29, 30, 31, 33, 35, 36, 37, 38, 40, 42, 43, 44, 45, 47, 49, 50, 51, 52, 54, 56, 57, 58, 59, 61, 63, 64, 65, 66, 68, 70, 71, 72, 73, 75, 77, 78, 79, 80, 82, 84, 85, 86, 87, 89, 91, 92 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

FORMULA

G.f.: x^2*(1+x+x^2+2*x^3+2*x^4)/ ( (x^4+x^3+x^2+x+1)*(x-1)^2 ). - R. J. Mathar, Dec 04 2011

From Wesley Ivan Hurt, Aug 08 2016: (Start)

a(n) = a(n-1) + a(n-5) - a(n-6) for n > 6.

a(n) = a(n-5) + 7 for n > 5.

a(n) = (35*n - 50 - 3*(n mod 5) + 2*((n+1) mod 5) + 2*((n+2) mod 5) + 2*((n+3) mod 5) - 3*((n+4) mod 5))/25.

a(5*k) = 7*k-2, a(5*k-1) = 7*k-4, a(5*k-2) = 7*k-5, a(5*k-3) = 7*k-6, a(5*k-4) = 7*k-7. (End)

MAPLE

A047373:=n->7*floor(n/5)+[(0, 1, 2, 3, 5)][(n mod 5)+1]: seq(A047373(n), n=0..100); # Wesley Ivan Hurt, Aug 08 2016

MATHEMATICA

Select[Range[0, 100], MemberQ[{0, 1, 2, 3, 5}, Mod[#, 7]] &] (* Wesley Ivan Hurt, Aug 08 2016 *)

LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 3, 5, 7}, 100] (* Vincenzo Librandi, Aug 08 2016 *)

PROG

(MAGMA) [n : n in [0..150] | n mod 7 in [0, 1, 2, 3, 5]]; // Wesley Ivan Hurt, Aug 08 2016

CROSSREFS

Sequence in context: A055977 A180221 A111292 * A039048 A105764 A226811

Adjacent sequences:  A047370 A047371 A047372 * A047374 A047375 A047376

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified July 30 04:51 EDT 2021. Contains 346348 sequences. (Running on oeis4.)