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

1,2

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.

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A000326, A000959, A031162, A118565.

Sequence in context: A259692 A204215 A164646 * A347922 A355418 A142994

Adjacent sequences: A128508 A128509 A128510 * A128512 A128513 A128514

Keyword

easy,nonn

Author

Jonathan Vos Post, May 07 2007

Extensions

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

Status

approved