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A111908
Numbers that are not the sum of a prime and a nonzero triangular number.
1
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
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 *)
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(47) and offset corrected by Donovan Johnson, Feb 09 2013
STATUS
approved