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%I #22 Oct 11 2016 12:21:03
%S 1,4,6,8,10,12,19,20,27,35,44,48,56,64,84,85,120,124,125,146,165,216,
%T 220,231,255,286,343,344,364,455,456,489,512,560,670,680,729,742,816,
%U 891,969,1000,1128,1140,1156,1330,1331,1469,1540,1629,1728,1771,1834
%N Platonic numbers: a(n) is a tetrahedral (A000292), cube (A000578), octahedral (A005900), dodecahedral (A006566) or icosahedral (A006564) number.
%C 19, the 3rd octahedral number, is the only prime platonic number. - _Jean-François Alcover_, Oct 11 2012
%H T. D. Noe, <a href="/A053012/b053012.txt">Table of n, a(n) for n = 1..1000</a>
%H OEIS Wiki, <a href="/wiki/Platonic_numbers">Platonic numbers</a>
%t nn = 25; t1 = Table[n (n + 1) (n + 2)/6, {n, nn}]; t2 = Table[n^3, {n, nn}]; t3 = Table[(2*n^3 + n)/3, {n, nn}]; t4 = Table[n (3*n - 1) (3*n - 2)/2, {n, nn}]; t5 = Table[n (5*n^2 - 5*n + 2)/2, {n, nn}]; Select[Union[t1, t2, t3, t4, t5], # <= t1[[-1]] &] (* _T. D. Noe_, Oct 13 2012 *)
%o (Haskell)
%o a053012 n = a053012_list !! (n-1)
%o a053012_list = tail $ f
%o [a000292_list, a000578_list, a005900_list, a006566_list, a006564_list]
%o where f pss = m : f (map (dropWhile (<= m)) pss)
%o where m = minimum (map head pss)
%o -- _Reinhard Zumkeller_, Jun 17 2013
%o (PARI) listpoly(lim, poly[..])=my(v=List()); for(i=1,#poly, my(P=poly[i], x=variable(P), f=k->subst(P,x,k),n,t); while((t=f(n++))<=lim, listput(v, t))); Set(v)
%o list(lim)=my(n='n); listpoly(lim, n*(n+1)*(n+2)/6, n^3, (2*n^3+n)/3, n*(3*n-1)*(3*n-2)/2, n*(5*n^2-5*n+2)/2) \\ _Charles R Greathouse IV_, Oct 11 2016
%Y Numbers of partitions into Platonic numbers: A226748, A226749.
%K easy,nice,nonn
%O 1,2
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 22 2000
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