A227727 a(n) is the least r>=3 such that the difference between n and the nearest r-gonal number<=n is an r-gonal number.

3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 5, 3, 7, 3, 3, 4, 3, 7, 4, 3, 3, 5, 3, 4, 4, 3, 3, 3, 11, 3, 16, 9, 3, 5, 3, 3, 19, 3, 4, 7, 3, 6, 22, 3, 3, 5, 3, 4, 4, 3, 5, 4, 19, 3, 3, 15, 3, 11, 6, 3, 7, 5, 4, 3, 3, 3, 4, 3, 5, 5, 3, 4, 37, 5, 3, 14, 3, 3, 4, 3, 4, 13

Offset: 0

Author

Vladimir Shevelev, Jul 30 2013

Keywords

• nonn

Comments

The n-th r-gonal number is n((n-1)r-2(n-2))/2, such that 3-gonal numbers are triangular numbers, 4-gonal numbers are squares, etc.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 0..1999

Crossrefs

Cf. A227321.

Programs

Mathematica

rGonalQ[r_,0]:=True; rGonalQ[r_,n_]:=IntegerQ[(Sqrt[((8r-16)n+(r-4)^2)]+r-4)/(2r-4)]; nthrGonal[r_,n_]:=(n (r-2)(n-1))/2+n; prevrGonal[r_,n_]:=nthrGonal[r,Floor[(Sqrt[((8r-16)n+(r-4)^2)]+r-4)/(2r-4)]]; (* previous r-gonal number greater than or equal to n *) Table[NestWhile[#+1&,3,!rGonalQ[#,n-prevrGonal[#,n]]&],{n,0,99}] (* Peter J. C. Moses, Aug 03 2013 *)

Extensions

More terms from Peter J. C. Moses, Jul 30 2013