

A032796


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


1



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
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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)/((1x)*(1x^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



