A111908 Numbers that are not the sum of a prime and a nonzero triangular number.

1, 2, 7, 36, 61, 105, 171, 210, 211, 216, 325, 351, 406, 528, 561, 630, 741, 780, 990, 1081, 1176, 1275, 1596, 1711, 1830, 1953, 2016, 2145, 2346, 2628, 2775, 3003, 3081, 3240, 3321, 3655, 3741, 3916, 4278, 4371, 4465, 4560, 4851, 5253, 5460, 5565, 5886

Offset

1,2

Comments

Can anybody prove or disprove a(n) = O(n^c) for some constant c?

Jonathan Vos Post has observed that every term in A076768 also occurs in this sequence.

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Example

7 = 1+6 = 2+5 = 3+4; 7 is in the sequence because there is no sum where the first element is a prime and the second one a triangular number.

Mathematica

lim=6000; plim=PrimePi[lim]; tlim=Ceiling[Sqrt[2lim]]; Complement[Range[lim], Union[Flatten[Table[Prime[i]+PolygonalNumber[j], {i, plim}, {j, tlim}]]]] (* James C. McMahon, Jun 04 2024 *)

Crossrefs

Cf. A064233, A000217, A076768, A020756, A072386, A014089, A014090, A000404, A001481, A002654, A100570, A101181.

Sequence in context: A247240 A266356 A196857 * A060814 A192816 A302895

Adjacent sequences: A111905 A111906 A111907 * A111909 A111910 A111911

Keyword

nonn

Author

Stefan Steinerberger, Nov 25 2005

Extensions

a(47) and offset corrected by Donovan Johnson, Feb 09 2013

Status

approved