A053012 Platonic numbers: a(n) is a tetrahedral (A000292), cube (A000578), octahedral (A005900), dodecahedral (A006566) or icosahedral (A006564) number.

1, 4, 6, 8, 10, 12, 19, 20, 27, 35, 44, 48, 56, 64, 84, 85, 120, 124, 125, 146, 165, 216, 220, 231, 255, 286, 343, 344, 364, 455, 456, 489, 512, 560, 670, 680, 729, 742, 816, 891, 969, 1000, 1128, 1140, 1156, 1330, 1331, 1469, 1540, 1629, 1728, 1771, 1834

Offset: 1

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Feb 22 2000

Keywords

• easy
• nice
• nonn

Comments

19, the 3rd octahedral number, is the only prime platonic number. - Jean-François Alcover, Oct 11 2012

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• OEIS Wiki, Platonic numbers

Crossrefs

Numbers of partitions into Platonic numbers: A226748, A226749.

Programs

Haskell

a053012 n = a053012_list !! (n-1)
a053012_list = tail $ f
   [a000292_list, a000578_list, a005900_list, a006566_list, a006564_list]
   where f pss = m : f (map (dropWhile (<= m)) pss)
                 where m = minimum (map head pss)
-- Reinhard Zumkeller, Jun 17 2013

Mathematica

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 *)

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)
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