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%I #44 Apr 08 2021 03:41:23
%S 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,
%T 53,56,59,61,62,67,68,71,73,74,77,79,80,83,86,89,97,98,101,103,104,
%U 107,109,110,113,116,119,122,127,128,131,134,137,139,140,143,146,149,151,152
%N Numbers which are not regular figurative or polygonal numbers of order greater than 2. That is, numbers not of the form 1 + k*n(n-1)/2 - (n-1)^2 where n >= 2 and k >= 2.
%C The n-th k-gonal number is 1 + k*n(n-1)/2 - (n-1)^2 = A057145(k,n).
%D Albert H. Beiler, Recreations In The Theory Of Numbers, The Queen Of Mathematics Entertains, Dover, NY, 1964, pp. 185-199.
%H Michel Marcus, <a href="/A090467/b090467.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FigurateNumber.html">Figurate Number.</a>
%H <a href="/index/Pol#polygonal_numbers">Index to sequences related to polygonal numbers</a>
%F An integer n >= 3 is in this sequence iff A176774(n) = n (or, equivalently, A176775(n) = 2). - _Max Alekseyev_, Apr 24 2018
%e 3 is a triangular number, but is not a k-gonal number for any other k, so 3 is a term.
%e 6 is both a triangular number and a hexagonal number, so 6 is not a term.
%t 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]]
%o (PARI) isok(n) = (n < 3) || (vecsum(vector(n-2, k, k+=2; ispolygonal(n, k))) == 1); \\ _Michel Marcus_, May 01 2016
%Y Complement is A090466.
%Y Cf. A057145, A176774, A176775.
%K easy,nonn
%O 1,2
%A _Robert G. Wilson v_, Dec 01 2003
%E Verified by _Don Reble_, Mar 12 2006
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