A003679 Numbers that are not the sum of 3 pentagonal numbers.

4, 8, 9, 16, 19, 20, 21, 26, 30, 31, 33, 38, 42, 43, 50, 54, 55, 60, 65, 67, 77, 81, 84, 88, 89, 90, 96, 99, 100, 101, 111, 112, 113, 120, 125, 131, 135, 138, 142, 154, 159, 160, 166, 170, 171, 183, 195, 204, 205, 207, 217, 224, 225, 226, 229, 230, 236, 240, 241

Offset: 1

Author

N. J. A. Sloane, Mira Bernstein

Keywords

• nonn
• easy
• nice

Comments

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

The next term, if it exists, is greater than 160000000. - Jack W Grahl, Jul 10 2018

a(211) > 10^11, if it exists. - Giovanni Resta, Jul 13 2018

References

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

Links

• T. D. Noe, Table of n, a(n) for n = 1..210
• J. W. Grahl, C code which was used to check for elements of this sequence up to 160,000,000.
• R. K. Guy, Every number is expressible as the sum of how many polygonal numbers?, Amer. Math. Monthly 101 (1994), 169-172.
• Eric Weisstein's World of Mathematics, Pentagonal Number

Crossrefs

Cf. A117065 (primes in this sequence).

Cf. A118278, A118279.

Programs

Mathematica

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 *)