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

1,2

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

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 *)

Prog

(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
(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

Crossrefs

Numbers of partitions into Platonic numbers: A226748, A226749.

Sequence in context: A307542 A225510 A131694 * A359202 A096160 A181055

Adjacent sequences: A053009 A053010 A053011 * A053013 A053014 A053015

Keyword

easy,nice,nonn

Author

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

Status

approved