A003679 - OEIS

%I M3323 #29 Jul 13 2018 05:10:53

%S 4,8,9,16,19,20,21,26,30,31,33,38,42,43,50,54,55,60,65,67,77,81,84,88,

%T 89,90,96,99,100,101,111,112,113,120,125,131,135,138,142,154,159,160,

%U 166,170,171,183,195,204,205,207,217,224,225,226,229,230,236,240,241

%N Numbers that are not the sum of 3 pentagonal numbers.

%C Guy's paper says that the sequence probably contains exactly 210 terms, six of which require five pentagonal numbers: 9, 21, 31, 43, 55 and 89. The last term is conjectured to be 33066. - _T. D. Noe_, Apr 19 2006

%C The next term, if it exists, is greater than 160000000. - _Jack W Grahl_, Jul 10 2018

%C a(211) > 10^11, if it exists. - _Giovanni Resta_, Jul 13 2018

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A003679/b003679.txt">Table of n, a(n) for n = 1..210</a>

%H J. W. Grahl, <a href="https://github.com/jwg4/oeis_misc/blob/master/c/a003679.c">C code which was used to check for elements of this sequence up to 160,000,000.</a>

%H R. K. Guy, <a href="http://www.jstor.org/stable/2324367">Every number is expressible as the sum of how many polygonal numbers?</a>, Amer. Math. Monthly 101 (1994), 169-172.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>

%t nn=200; pen=Table[n(3n-1)/2, {n,0,nn-1}]; lst=Range[pen[[ -1]]; Do[n=pen[[i]]+pen[[j]]+pen[[k]]; If[n<=pen[[ -1]], lst=DeleteCases[lst,n]]], {i,nn}, {j,i,nn}, {k,j,nn}]; lst (* _T. D. Noe_, Apr 19 2006 *)

%Y Cf. A117065 (primes in this sequence).

%Y Cf. A118278, A118279.

%K nonn,easy,nice

%O 1,1

%A _N. J. A. Sloane_, _Mira Bernstein_