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A090466 Regular figurative or polygonal numbers of order greater than 2. 8
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.

Sequence A090428 (excluding 1) is a subset of this sequence. - T. D. Noe, Jun 14 2012

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

REFERENCES

Albert H. Beiler, Recreations In The Theory Of Numbers, The Queen Of Mathematics Entertains, Dover, NY, 1964, pps. 185-199.

LINKS

T. D. Noe and Robert G. Wilson v, Table of n, a(n) for n = 1..10000 (only the first 1000 terms are from T. D. Noe).

Eric Weisstein's World of Mathematics, Figurate Number

Index to sequences related to polygonal numbers

FORMULA

The n-th k-gonal number is 1 + k*n(n-1)/2 - (n-1)^2 = A057145(k,n).

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 *)

planeFigurative1[ngon_, rank_]:=(ngon-2) Binomial[rank, 2]+rank; mx = 150; n = k = 3; lst = {}; While[n < Floor[mx/3]+2, a = planeFigurative1[n, k]; If[a < mx+1, AppendTo[ lst, a], (n++; k = 2)]; k++]; lst = Union@ lst (* Robert G. Wilson v, May 29 2014 *)

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

CROSSREFS

Cf. A057145. Complement is A090467.

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 (djr(AT)nk.ca), Mar 12 2006

STATUS

approved

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Last modified March 23 01:23 EDT 2017. Contains 283901 sequences.