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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
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
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
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jul 30 2013
EXTENSIONS
More terms from Peter J. C. Moses, Jul 30 2013
STATUS
approved