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

%I A275340 #40 Jun 19 2023 12:40:52
%S A275340 4,7,10,11,13,16,19,21,22,25,28,29,31,34,37,40,41,43,46,49,51,52,55,
%T A275340 56,57,58,61,64,67,70,71,73,76,79,81,82,85,88,91,92,94,97,100,101,103,
%U A275340 106,109,111,112,113,115,118,121,124,127,130,131,133,136,137,139,141,142,145,148,151
%N A275340 Nontrivial centered polygonal numbers: numbers of the form A101321(n,k) where n >= 1 and k >= 2.
%C A275340 This is a centered polygonal number analog to A090466.
%H A275340 Charles R Greathouse IV, <a href="/A275340/b275340.txt">Table of n, a(n) for n = 1..10000</a>
%F A275340 a(n) ~ c*n with 1.95 < c < 2.29. - _Charles R Greathouse IV_, Jul 28 2016
%p A275340 isA275340 := proc(n)
%p A275340     local nsearch,ksearch;
%p A275340     for nsearch from 1 do
%p A275340         if A101321(nsearch,2) > n then
%p A275340             return false;
%p A275340         end if;
%p A275340         for ksearch from 2 do
%p A275340             if A101321(nsearch,ksearch) = n then
%p A275340                 return true;
%p A275340             elif A101321(nsearch,ksearch) > n then
%p A275340                 break;
%p A275340             end if;
%p A275340         end do:
%p A275340     end do:
%p A275340 end proc:
%p A275340 for n from 1 to 400 do
%p A275340     if isA275340(n) then
%p A275340         printf("%d,",n) ;
%p A275340     end if;
%p A275340 end do:
%t A275340 maxTerm = 1000;
%t A275340 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 *)
%o A275340 (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
%Y A275340 Cf. A101321.
%K A275340 nonn
%O A275340 1,1
%A A275340 _R. J. Mathar_, Jul 28 2016