A128511 Numbers which are both lucky and pentagonal.

1, 51, 477, 651, 925, 2625, 5551, 6501, 9801, 17767, 20475, 25285, 26467, 29751, 39285, 45327, 67947, 75825, 84135, 84847, 95887, 99717, 102051, 114955, 135751, 151527, 154401, 178365, 245835, 261877, 272001, 275847, 287547, 292825, 307587

Offset: 1

Author

Jonathan Vos Post, May 07 2007

Keywords

• easy
• nonn

Comments

Second row of array T(k,n) = n-th Lucky number which is also a (k+3)-gonal number, for nonnegative k, whose zeroth and first rows are: A118565 Numbers which are both lucky and triangular. A031162 Numbers that are both lucky and square.

Examples

			a(2) = 51 = A000959(14) = A000326(6).
a(3) = 477 = A000959(81) = A000326(18).
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1244 (terms < 10^9)

Crossrefs

Cf. A000326, A000959, A031162, A118565.

Programs

Maple

isA000326 := proc(n) local di ; if issqr(1+24*n) or n =0 then di := 1+sqrt(1+24*n); if di mod 6 = 0 or n = 0 then true ; else false ; fi ; else false ; fi; end: lin := fscanf("b000959.txt","%d %d") : while lin <> [] do a := op(2,lin) ; if isA000326( a ) then printf("%d, ",a) ; fi ; lin := fscanf("b000959.txt","%d %d") ; od : # R. J. Mathar, May 13 2007

Mathematica

lim=320000;lp=Ceiling[Sqrt[2lim/3]];lL=lim/2;p=Array[# (3 # - 1)/2 &, lp, 0] ;L = Table[2*i + 1, {i, 0, lL}]; For[n = 2, n < Length[L], r = L[[n++]]; L = ReplacePart[L, Table[r*i -> Nothing, {i, 1, Length[L]/r}]]];Select[Range[lim],MemberQ[p,#]&&MemberQ[L,#]&] (* James C. McMahon, Jan 09 2025 *)

Formula

A000959 INTERSECTION A000326 = A000959 INTERSECTION {n*(3*n-1)/2}.

Extensions

More terms from R. J. Mathar, May 13 2007