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A090466
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Regular figurative or polygonal numbers of order greater than 2.
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5
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6, 9, 10, 12, 15, 16, 18, 21, 22, 24, 25, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 63, 64, 65, 66, 69, 70, 72, 75, 76, 78, 81, 82, 84, 85, 87, 88, 90, 91, 92, 93, 94, 95, 96, 99, 100, 102, 105, 106, 108, 111, 112, 114, 115, 117, 118
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The sorted k-gonal numbers of order greater than 2. If you were to include the either the rank 2 or the 2-gonal numbers, then no number would be excluded.
Essentially the same as A090428. - Ant King, Sep 19 2011
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REFERENCES
| Albert H. Beiler, Recreations In The Theory Of Numbers, The Queen Of Mathematics Entertains, Dover, NY, 1964, pps. 185-199.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Figurate Number
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FORMULA
| The n-th k-gonal number is 1 +k*n(n-1)/2 - (n-1)^2.
Just as the number of primes under x can be approximated by the function Li(x), the number of "regular figurative" numbers under x can be approximated (to a much higher degree of accuracy) using the function that you can find here: donblazys.com/on_polygonal_numbers.pdf (or by Google searching "don blazys polygonal number counting function"). Would it be possible to calculate a table of how many "regular figurative" numbers there are under, say, x=10^20 ? Such a table would be very usefull and may yield some interesting results. [From Don Blazys (donblazys(AT)gmail.com), Aug 19 2010]
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MATHEMATICA
| Take[Union[Flatten[Table[1+k*n (n-1)/2-(n-1)^2, {n, 3, 100}, {k, 3, 40}]]], 67] (* corrected by Ant King, Sep 19 2011 *)
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CROSSREFS
| Complement is A090467.
Specific polygonal numbers: A000217, A000290, A000326, A000384, A000566, A000567, A001106, A001107, A051682, A051624, A051865-A051876.
Sequence in context: A053869 A085275 A177201 * A090428 A039725 A125494
Adjacent sequences: A090463 A090464 A090465 * A090467 A090468 A090469
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KEYWORD
| easy,nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 01 2003
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EXTENSIONS
| Verified by Don Reble (djr(AT)nk.ca), Mar 12 2006
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