

A090467


Numbers which are not regular figurative or polygonal numbers of order greater than 2. That is, numbers not of the form 1 + k*n(n1)/2  (n1)^2 where n >= 2 and k >= 2.


9



1, 2, 3, 4, 5, 7, 8, 11, 13, 14, 17, 19, 20, 23, 26, 29, 31, 32, 37, 38, 41, 43, 44, 47, 50, 53, 56, 59, 61, 62, 67, 68, 71, 73, 74, 77, 79, 80, 83, 86, 89, 97, 98, 101, 103, 104, 107, 109, 110, 113, 116, 119, 122, 127, 128, 131, 134, 137, 139, 140, 143, 146, 149, 151, 152
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OFFSET

1,2


COMMENTS

The nth kgonal number is 1 + k*n(n1)/2  (n1)^2 = A057145(k,n).


REFERENCES

Albert H. Beiler, Recreations In The Theory Of Numbers, The Queen Of Mathematics Entertains, Dover, NY, 1964, pp. 185199.


LINKS

Michel Marcus, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
Eric Weisstein's World of Mathematics, Figurate Number.
Index to sequences related to polygonal numbers


FORMULA

An integer n >= 3 is in this sequence iff A176774(n) = n (or, equivalently, A176775(n) = 2).  Max Alekseyev, Apr 24 2018


EXAMPLE

3 is a triangular number, but is not a kgonal number for any other k, so 3 is a term.
6 is both a triangular number and a hexagonal number, so 6 is not a term.


MATHEMATICA

Complement[ Table[i, {i, 300}], Take[ Union[ Flatten[ Table[1 + k*n(n  1)/2  (n  1)^2, {n, 3, 40}, {k, 3, 300}]]], 300]]


PROG

(PARI) isok(n) = (n < 3)  (vecsum(vector(n2, k, k+=2; ispolygonal(n, k))) == 1); \\ Michel Marcus, May 01 2016


CROSSREFS

Complement is A090466.
Cf. A057145, A176774, A176775.
Sequence in context: A062890 A259626 A058586 * A177202 A053868 A241912
Adjacent sequences: A090464 A090465 A090466 * A090468 A090469 A090470


KEYWORD

easy,nonn


AUTHOR

Robert G. Wilson v, Dec 01 2003


EXTENSIONS

Verified by Don Reble, Mar 12 2006


STATUS

approved



