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A165718 Integers of the form k*(k+7)/6. 3
3, 5, 10, 13, 20, 24, 33, 38, 49, 55, 68, 75, 90, 98, 115, 124, 143, 153, 174, 185, 208, 220, 245, 258, 285, 299, 328, 343, 374, 390, 423, 440, 475, 493, 530, 549, 588, 608, 649, 670, 713, 735, 780, 803, 850, 874, 923, 948, 999, 1025, 1078, 1105, 1160, 1188 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Integers of the form k+k*(k+1)/6 = k+A000217(k)/3; for k see A007494, for A000217(k)/3 see A001318 - R. J. Mathar, Sep 25 2009

Only 3 terms are prime numbers (3,5,13). Are all the rest composite?

LINKS

Table of n, a(n) for n=1..54.

FORMULA

a(n)= a(n-1) +2*a(n-2) -2*a(n-3) -a(n-4) +a(n-5) - R. J. Mathar, Sep 25 2009

G.f.: x*(-3-2*x+x^2+x^3)/((1+x)^2 * (x-1)^3 ). - R. J. Mathar, Sep 25 2009

EXAMPLE

For k=1, 2,3,.. k*(k+7)/6 is 4/3, 3, 5, 22/3, 10, 13, 49/3, 20, 24, 85/3, 33,.., and the integer values out of these become the sequence.

MATHEMATICA

q=3; s=0; lst={}; Do[s+=((n+q)/q); If[IntegerQ[s], AppendTo[lst, s]], {n, 6!}]; lst

CROSSREFS

Cf. A165717

Sequence in context: A034746 A275219 A080931 * A031878 A265282 A160792

Adjacent sequences:  A165715 A165716 A165717 * A165719 A165720 A165721

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, Sep 24 2009

EXTENSIONS

Definition simplified by R. J. Mathar, Sep 25 2009

STATUS

approved

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Last modified December 10 17:19 EST 2016. Contains 279005 sequences.