A032796 Numbers that are congruent to {1, 2, 3, 5, 6} mod 7.

1, 2, 3, 5, 6, 8, 9, 10, 12, 13, 15, 16, 17, 19, 20, 22, 23, 24, 26, 27, 29, 30, 31, 33, 34, 36, 37, 38, 40, 41, 43, 44, 45, 47, 48, 50, 51, 52, 54, 55, 57, 58, 59, 61, 62, 64, 65, 66, 68, 69, 71, 72, 73, 75, 76, 78, 79, 80, 82, 83, 85, 86, 87, 89, 90, 92, 93, 94, 96, 97, 99

Offset

1,2

Comments

If k is a term, then k*(k+1)*(k+2)*...*(k+6)/(k+(k+1)+(k+2)+...+(k+6)) is a multiple of k.

Links

Table of n, a(n) for n=1..71.

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

Formula

Equals natural numbers minus '4, 7, 11, 14, 18, ...' (= previous term +3, +4, +3, +4, ...).

G.f.: x*(x^5 + x^4 + 2*x^3 + x^2 + x + 1)/((1-x)*(1-x^5)).

a(n) = (m^3 - 6*m^2 + 17*m + 6*(7*floor(n/5)-1))/6, where m = n mod 5. - Luce ETIENNE,Oct 17 2018

Mathematica

#+{1, 2, 3, 5, 6}&/@(7*Range[0, 15])//Flatten (* or *) LinearRecurrence[ {1, 0, 0, 0, 1, -1}, {1, 2, 3, 5, 6, 8}, 100] (* Harvey P. Dale, Oct 07 2018 *)

Prog

(Magma) [n: n in [0..120] | n mod 7 in {1, 2, 3, 5, 6}]; // Vincenzo Librandi, Dec 29 2010

Crossrefs

Cf. A032765..A032798.

Cf. A010874.

Sequence in context: A247431 A039033 A047333 * A087057 A184580 A184622

Adjacent sequences: A032793 A032794 A032795 * A032797 A032798 A032799

Keyword

nonn,easy

Author

Patrick De Geest, May 15 1998

Status

approved