A118565 -id:A118565 - cp's OEIS frontend

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

Jonathan Vos Post, May 07 2007

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.

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

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

Cf. A000326, A000959, A031162, A118565.

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

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 *)

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

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

A225322 Lucky numbers that are prime powers.

Original entry on oeis.org

1, 9, 25, 49, 169, 289, 361, 529, 729, 841, 961, 1369, 2187, 2209, 3481, 3721, 5041, 7921, 9409, 10609, 24649, 29791, 32041, 32761, 36481, 50653, 52441, 66049, 73441, 83521, 113569, 121801, 128881, 130321, 167281, 175561, 185761, 226981, 292681, 300763, 323761

Offset: 1

Alex Ratushnyak, May 05 2013

nonn

Intersection of A025475 and A000959.

Conjecture: the sequence is infinite.

Kevin P. Thompson, Table of n, a(n) for n = 1..1577 (terms < 10^10 with terms 1..628 from Donovan Johnson)

Cf. A000959, A025475.

Cf. A031157, A031162, A057589, A118565, A128511.

A128947 Main diagonal of polygonal lucky array defined in A128511.

Original entry on oeis.org

1, 9, 477, 2415, 2059, 2133, 651, 2835, 14935, 23529, 35721, 58311, 27105, 24013, 167775, 49375, 92925, 193305, 273105, 238855, 850155, 94209, 395901, 1055241, 310233, 387001, 1492839, 540765, 731025, 2172081, 934431, 835621

Offset: 1

Jonathan Vos Post, May 09 2007, May 23 2007

Main diagonal of array T(k,n) = n-th lucky number which is also a (k+3)-gonal number, for nonnegative k, whose zeroth, first, second rows are: A118565 Numbers which are both lucky and triangular. A031162 Numbers that are both lucky and square. A128511 Numbers which are both lucky and pentagonal.

			Array begins:
k..|.n-th lucky number which is also a (k+3)-gonal number
0..|.1...3...15....21...105...171...231...741...903..1275.
1..|.1...9...25....49...169...289...361...529...729...841.
2..|.1..51..477...651...925..2625..5551..6501..9801.17767.
3..|.1..15..231..2415..3003..3655..5151.10585.11781.13695.
4..|.1...7..189...235..2059..6175..8037..9211.17935.23377.
5..|.1..21..133...645..1281..2133..2821..4033..4485..7701.
6..|.1...9...75...111...261...559...651..1491..1639..2125.
7..|.1.297..451...855..1105..1387..1701..2835..4257..5967.

Cf. A000567, A000959, A031162, A118565, A128511.

findpl(vl, n) = {nb = 0; for (i=1, #vl, if (ispolygonal(vl[i], n+2), nb++; if (nb == n, return (vl[i]))););}
lista(nn) = {vl = readvec("b000959.log"); for (n=1, nn, print1(findpl(vl, n), ", "););} \\ Michel Marcus, Mar 04 2014

More terms from R. J. Mathar, Jun 07 2007
6 more terms via b000959.txt from R. J. Mathar, Oct 22 2010
a(21)-a(32) via b000959.txt from Michel Marcus, Mar 04 2014

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A128511 Numbers which are both lucky and pentagonal.

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A225322 Lucky numbers that are prime powers.

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A128947 Main diagonal of polygonal lucky array defined in A128511.

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