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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. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The n-th r-gonal numbers 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: A105159 A209291 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

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Last modified June 19 17:38 EDT 2019. Contains 324222 sequences. (Running on oeis4.)