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A067589 Numbers k such that A067588(k) is an odd number. 5
1, 5, 7, 15, 35, 51, 57, 77, 117, 145, 155, 187, 247, 287, 301, 345, 425, 477, 495, 551, 651, 715, 737, 805, 925, 1001, 1027, 1107, 1247, 1335, 1365, 1457, 1617, 1717, 1751, 1855, 2035, 2147, 2185, 2301, 2501, 2625, 2667, 2795, 3015, 3151, 3197, 3337 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The terms are exactly the odd pentagonal numbers; that is, they are all the odd numbers of the form k*(3*k-1)/2 where k is an integer. - James A. Sellers, Jun 09 2007
Apparently groups of two odd pentagonal numbers (A000326, A014632) followed by two odd 2nd pentagonal numbers (A005449), which leads to the conjectured generating function x*(x^2+4*x+1)*(x^4-2*x^3+4*x^2-2*x+1)/((x^2+1)^2*(1-x)^3). - R. J. Mathar, Jul 26 2009
Odd generalized pentagonal numbers. - Omar E. Pol, Aug 19 2011
LINKS
FORMULA
Sum_{n>=1} 1/a(n) = Pi/2. - Amiram Eldar, Aug 18 2022
MATHEMATICA
With[{nn=50}, Sort[Select[Table[(n(3n-1))/2, {n, -nn, nn}], OddQ]]] (* Harvey P. Dale, Feb 16 2014 *)
CROSSREFS
Cf. A001318, A193828. - Omar E. Pol, Aug 19 2011
Sequence in context: A003429 A076860 A283592 * A059613 A242503 A116048
KEYWORD
nonn,easy
AUTHOR
Naohiro Nomoto, Jan 31 2002
EXTENSIONS
Corrected by T. D. Noe, Oct 25 2006
STATUS
approved

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Last modified April 14 20:39 EDT 2024. Contains 371667 sequences. (Running on oeis4.)