The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A090466 Regular figurative or polygonal numbers of order greater than 2. 16
 6, 9, 10, 12, 15, 16, 18, 21, 22, 24, 25, 27, 28, 30, 33, 34, 35, 36, 39, 40, 42, 45, 46, 48, 49, 51, 52, 54, 55, 57, 58, 60, 63, 64, 65, 66, 69, 70, 72, 75, 76, 78, 81, 82, 84, 85, 87, 88, 90, 91, 92, 93, 94, 95, 96, 99, 100, 102, 105, 106, 108, 111, 112, 114, 115, 117, 118 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sorted k-gonal numbers of order greater than 2. If one were to include either the rank 2 or the 2-gonal numbers, then every number would appear. Number of terms less than or equal to 10^k for k = 1,2,3,...: 3, 57, 622, 6357, 63889, 639946, 6402325, 64032121, 640349979, 6403587409, 64036148166, 640362343980, ..., . - Robert G. Wilson v, May 29 2014 The n-th k-gonal number is 1 + k*n(n-1)/2 - (n-1)^2 = A057145(k,n). For all squares (A001248) of primes p >= 5 at least one a(n) exists with p^2 = a(n) + 1. Thus the subset P_s(3) of rank 3 only is sufficient. Proof: For p >= 5, p^2 == 1 (mod {3,4,6,8,12,24}) and also P_s(3) + 1 = 3*s - 2 == 1 (mod 3). Thus the set {p^2} is a subset of {P_s(3) + 1}; Q.E.D. - Ralf Steiner, Jul 15 2018 For all primes p > 5, at least one polygonal number exists with P_s(k) + 1 = p when k = 3 or 4, dependent on p mod 6. - Ralf Steiner, Jul 16 2018 Numbers m such that r = (2*m/d - 2)/(d - 1) is an integer for some d, where 2 < d < m is a divisor of 2*m. If r is an integer, then m is the d-th (r+2)-gonal number. - Jianing Song, Mar 14 2021 REFERENCES Albert H. Beiler, Recreations In The Theory Of Numbers, The Queen Of Mathematics Entertains, Dover, NY, 1964, pp. 185-199. LINKS Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (first 1000 terms are from T. D. Noe) Eric Weisstein's World of Mathematics, Figurate Number FORMULA Integer k is in this sequence iff A176774(k) < k. - Max Alekseyev, Apr 24 2018 MAPLE isA090466 := proc(n)     local nsearch, ksearch;     for nsearch from 3 do         if A057145(nsearch, 3) > n then             return false;         end if;         for ksearch from 3 do             if A057145(nsearch, ksearch) = n then                 return true;             elif A057145(nsearch, ksearch) > n then                 break;             end if;         end do:     end do: end proc: for n from 1 to 1000 do     if isA090466(n) then         printf("%d, ", n) ;     end if; end do: # R. J. Mathar, Jul 28 2016 MATHEMATICA Take[Union[Flatten[Table[1+k*n (n-1)/2-(n-1)^2, {n, 3, 100}, {k, 3, 40}]]], 67] (* corrected by Ant King, Sep 19 2011 *) mx = 150; n = k = 3; lst = {}; While[n < Floor[mx/3]+2, a = PolygonalNumber[n, k]; If[a < mx+1, AppendTo[ lst, a], (n++; k = 2)]; k++]; lst = Union@ lst (* Robert G. Wilson v, May 29 2014 and updated Jul 23 2018; PolygonalNumber requires version 10.4 or higher *) PROG (PARI) list(lim)=my(v=List()); lim\=1; for(n=3, sqrtint(8*lim+1)\2, for(k=3, 2*(lim-2*n+n^2)\n\(n-1), listput(v, 1+k*n*(n-1)/2-(n-1)^2))); Set(v); \\ Charles R Greathouse IV, Jan 19 2017 (PARI) is(n)=for(s=3, n\3+1, ispolygonal(n, s)&&return(s)); \\ M. F. Hasler, Jan 19 2017 (PARI) isA090466(m) = my(v=divisors(2*m)); for(i=3, #v, my(d=v[i]); if(d==m, return(0)); if((2*m/d - 2)%(d - 1)==0, return(1))); 0 \\ Jianing Song, Mar 14 2021 CROSSREFS Cf. A057145, A001248. Complement is A090467. Sequence A090428 (excluding 1) is a subsequence of this sequence. - T. D. Noe, Jun 14 2012 Sequence in context: A053869 A085275 A177201 * A090428 A039725 A262362 Adjacent sequences:  A090463 A090464 A090465 * A090467 A090468 A090469 KEYWORD easy,nonn AUTHOR Robert G. Wilson v, Dec 01 2003 EXTENSIONS Verified by Don Reble, Mar 12 2006 STATUS approved

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

Last modified September 30 20:49 EDT 2022. Contains 357106 sequences. (Running on oeis4.)