login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A227321 a(n) is the least r>=3 such that the difference between the nearest r-gonal number >= n and n is an r-gonal number. 3
3, 3, 3, 3, 4, 3, 3, 3, 4, 3, 3, 5, 3, 8, 3, 3, 4, 5, 3, 11, 3, 3, 3, 5, 4, 3, 10, 3, 3, 11, 3, 17, 4, 3, 5, 3, 3, 7, 14, 3, 4, 15, 3, 23, 3, 3, 5, 11, 4, 3, 5, 5, 3, 19, 3, 3, 3, 8, 5, 21, 3, 32, 14, 3, 4, 3, 3, 15, 3, 5, 5, 25, 3, 38, 7, 3, 6, 3, 3, 13, 4, 3 (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

FORMULA

If n is prime, then n == 1 or 2 mod (a(n)-2). If n >= 13 is the greater of a pair of twin primes (A006512), then a(n) = (n+3)/2. - Vladimir Shevelev, Aug 07 2013

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

CROSSREFS

Cf. A000217 (r=3), A000290 (r=4), A000326 (r=5), A000384 (r=6), A000566 (r=7), A000567 (r=8), A001106-7 (r=9,10), A051682 (r=11), A051624 (r=12), A051865-A051876 (r=13-24).

Sequence in context: A048181 A091799 A276863 * A309555 A262994 A179847

Adjacent sequences:  A227318 A227319 A227320 * A227322 A227323 A227324

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Jul 30 2013

EXTENSIONS

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

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 30 05:03 EDT 2020. Contains 337435 sequences. (Running on oeis4.)