A375249 Integers which cannot be partitioned into the sum of a hexagonal number plus a pentagonal number, nor a hexagonal number plus a square, nor a pentagonal number plus a square.
3, 8, 34, 43, 56, 59, 62, 68, 72, 73, 83, 89, 90, 97, 104, 110, 111, 114, 131, 138, 139, 148, 152, 163, 164, 167, 168, 186, 193, 200, 203, 205, 207, 222, 227, 228, 229, 233, 244, 249, 250, 252, 258, 269, 273, 279, 299, 300, 305, 306, 308, 309, 318, 319, 321, 333, 343, 344, 356, 364, 365
Offset: 1
Examples
7 is not in the sequence since the third hexagonal number 6 plus the second square or pentagonal number sum to 7;
8 is in the sequence because s = {0, 1, 4}, p = {0, 1, 5}, and h = {0, 1, 6} with no two sets having members which sum to 8.
Links
- Robert G. Wilson v, Table of n, a(n) for n = 1..10000
- Zhi-Wei Sun, On universal sums of polygonal numbers, arXiv:0905.0635 [math.NT], 2009-2015.
Programs
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Mathematica
planeFiguratePi[r_,n_] := Floor[((r -4) +Sqrt[(r -4)^2 + 8n (r -2)])/(2 (r - 2))]; h = Table[PolygonalNumber[6, n], {n, 0, planeFiguratePi[6, 500]}]; p = Table[PolygonalNumber[5, n], {n, 0, planeFiguratePi[5, 500]}]; s = Table[PolygonalNumber[4, n], {n, 0, planeFiguratePi[4, 500]}]; Complement[ Range@ 500, Flatten[{Outer[Plus, h, p], Outer[Plus, h, s], Outer[Plus, p, s]} ]]
Comments