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a(1)=1, a(n) = least odd triangular number which is a proper multiple of a(n-1).
1

%I #12 Sep 25 2023 04:55:51

%S 1,3,15,45,1035,85905,1116765,657774585,16566052923225,

%T 1679075536205721159675,5080495373624679083985366566435450475,

%U 61777199356706369989502028371103145170633166772200816412636015025

%N a(1)=1, a(n) = least odd triangular number which is a proper multiple of a(n-1).

%o (PARI) my(v=[1, 3, 15, 45, 1035]); for (i=1, #v, print1(v[i], ", ")); n = 1035; for (j = 1, 8, f = factor(n); m = matsize(f)[1]; a = vector(2^m); count = 0; moz = vector(m, x, [ -1, 0]); forvec(x = moz, count++; r = chinese(Mod(x[1], f[1, 1]^f[1, 2]), Mod(x[2], f[2, 1]^f[2, 2])); for (i = 3, m, r = chinese(r, Mod(x[i], f[i, 1]^f[i, 2]))); a[count] = lift(r)); a = vecsort(a); b = vector(2^m, i, a[i]*(a[i] + 1)/2); i = 3; while (!(b[i]%2), i++); n = b[i]; print1(n, ", ")); \\ _David Wasserman_, Jul 20 2005

%Y Cf. A014493 (odd triangular numbers).

%K nonn

%O 1,2

%A _Amarnath Murthy_, Sep 24 2003

%E More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Aug 25 2004

%E 3 more terms from _David Wasserman_, Jul 20 2005