A275340 Nontrivial centered polygonal numbers: numbers of the form A101321(n,k) where n >= 1 and k >= 2.

4, 7, 10, 11, 13, 16, 19, 21, 22, 25, 28, 29, 31, 34, 37, 40, 41, 43, 46, 49, 51, 52, 55, 56, 57, 58, 61, 64, 67, 70, 71, 73, 76, 79, 81, 82, 85, 88, 91, 92, 94, 97, 100, 101, 103, 106, 109, 111, 112, 113, 115, 118, 121, 124, 127, 130, 131, 133, 136, 137, 139, 141, 142, 145, 148, 151

Offset: 1

Author

R. J. Mathar, Jul 28 2016

Keywords

• nonn

Comments

This is a centered polygonal number analog to A090466.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A101321.

Programs

Maple

isA275340 := proc(n)
    local nsearch,ksearch;
    for nsearch from 1 do
        if A101321(nsearch,2) > n then
            return false;
        end if;
        for ksearch from 2 do
            if A101321(nsearch,ksearch) = n then
                return true;
            elif A101321(nsearch,ksearch) > n then
                break;
            end if;
        end do:
    end do:
end proc:
for n from 1 to 400 do
    if isA275340(n) then
        printf("%d,",n) ;
    end if;
end do:

Mathematica

maxTerm = 1000;
Table[1+n*k*(k+1)/2, {n, 1, maxTerm-1}, {k, 2, Sqrt[2maxTerm] // Ceiling}] // Flatten // Union // Select[#, # <= maxTerm&]& (* Jean-François Alcover, Jun 17 2023 *)

PARI

list(lim)=my(v=List(),t); lim\=1; for(k=2,sqrt(8*lim-7)/2, t=k*(k+1)/2; forstep(a=t+1,lim,t, listput(v,a))); Set(v) \\ Charles R Greathouse IV, Jul 28 2016

Formula

a(n) ~ c*n with 1.95 < c < 2.29. - Charles R Greathouse IV, Jul 28 2016