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

0,1

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

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 *)

Crossrefs

Cf. A227321.

Sequence in context: A375642 A332875 A176873 * A050499 A304431 A147752

Adjacent sequences: A227724 A227725 A227726 * A227728 A227729 A227730

Keyword

nonn

Author

Vladimir Shevelev, Jul 30 2013

Extensions

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

Status

approved