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A165719 Integers of the form k*(k+9)/8. 2
14, 17, 45, 50, 92, 99, 155, 164, 234, 245, 329, 342, 440, 455, 567, 584, 710, 729, 869, 890, 1044, 1067, 1235, 1260, 1442, 1469, 1665, 1694, 1904, 1935, 2159, 2192, 2430, 2465, 2717, 2754, 3020, 3059, 3339, 3380, 3674, 3717, 4025, 4070, 4392, 4439, 4775 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Only one term is a prime number (17). Are all others composite?

Integers of the form k+k*(k+1)/8 = k+A000217(k)/4; for k see A047521, for A000217(k)/4 see A154260.

LINKS

Table of n, a(n) for n=1..47.

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

a(n)= 2*n^2+6*n+9/4-3*(-1)^n*(2*n+3)/4. - R. J. Mathar, Sep 25 2009

G.f.: x*(-14-3*x+x^3)/((1+x)^2 * (x-1)^3 ). - R. J. Mathar, Sep 25 2009

EXAMPLE

for k = 1,2,..., k(k+9)/8 is 5/4, 11/4, 9/2, 13/2, 35/4, 45/4, 14, 17,.. and the integer values out of these become the sequence.

MATHEMATICA

q=4; s=0; lst={}; Do[s+=((n+q)/q); If[IntegerQ[s], AppendTo[lst, s]], {n, 6!}]; lst

CROSSREFS

Cf. A165717, A165718

Sequence in context: A102816 A303305 A236685 * A154146 A113735 A063828

Adjacent sequences:  A165716 A165717 A165718 * A165720 A165721 A165722

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 November 21 22:35 EST 2019. Contains 329383 sequences. (Running on oeis4.)