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%I #9 Mar 04 2014 06:59:52
%S 1,9,477,2415,2059,2133,651,2835,14935,23529,35721,58311,27105,24013,
%T 167775,49375,92925,193305,273105,238855,850155,94209,395901,1055241,
%U 310233,387001,1492839,540765,731025,2172081,934431,835621
%N Main diagonal of polygonal lucky array defined in A128511.
%C 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.
%e Array begins:
%e k..|.n-th lucky number which is also a (k+3)-gonal number
%e 0..|.1...3...15....21...105...171...231...741...903..1275.
%e 1..|.1...9...25....49...169...289...361...529...729...841.
%e 2..|.1..51..477...651...925..2625..5551..6501..9801.17767.
%e 3..|.1..15..231..2415..3003..3655..5151.10585.11781.13695.
%e 4..|.1...7..189...235..2059..6175..8037..9211.17935.23377.
%e 5..|.1..21..133...645..1281..2133..2821..4033..4485..7701.
%e 6..|.1...9...75...111...261...559...651..1491..1639..2125.
%e 7..|.1.297..451...855..1105..1387..1701..2835..4257..5967.
%o (PARI) findpl(vl, n) = {nb = 0; for (i=1, #vl, if (ispolygonal(vl[i], n+2), nb++; if (nb == n, return (vl[i]))););}
%o lista(nn) = {vl = readvec("b000959.log"); for (n=1, nn, print1(findpl(vl, n), ", "););} \\ _Michel Marcus_, Mar 04 2014
%Y Cf. A000567, A000959, A031162, A118565, A128511.
%K more,nonn
%O 1,2
%A _Jonathan Vos Post_, May 09 2007, May 23 2007
%E More terms from _R. J. Mathar_, Jun 07 2007
%E 6 more terms via b000959.txt from _R. J. Mathar_, Oct 22 2010
%E a(21)-a(32) via b000959.txt from _Michel Marcus_, Mar 04 2014
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