# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a068513 Showing 1-1 of 1 %I A068513 #10 May 06 2024 11:04:13 %S A068513 15,45,630,25200,32004000,508031496000,128015872500032496000, %T A068513 3670698694547655407496988066168944000, %U A068513 10302657959650317880463349610273001290502485245258650172717840000 %N A068513 a(0) = 15; for n > 0, a(n) is the smallest triangular number which is a (proper) multiple of a(n-1). %C A068513 Thanks to _Dean Hickerson_ for a very efficient program. %H A068513 Chai Wah Wu, Table of n, a(n) for n = 0..10 %t A068513 Needs[ NumberTheory`NumberTheoryFunctions`]; pm1[{k_}] := {1, k - 1}; pm1[lst_] := Module[{a, m, v}, a = lst[[1]]; m = Times @@ Rest[lst]; v = pm1[ Rest[lst]]; Union[ ChineseRemainder[{1, #}, {a, m}] & /@ v, ChineseRemainder[{-1, #}, {a, m}] & /@ v]]; nexttri[1] = 3; nexttri[n_] := Module[{s}, s = (pm1[Power @@ # & /@ FactorInteger[4n]]^2 - 1)/8; For[i = 1, True, i++, If[s[[i]] > n, Return[ s[[i]]] ]]]; a[0] = 15; a[n_] := a[n] = nexttri[ a[n - 1]]; Table[ a[n], {n, 0, 8}] %o A068513 (Python) %o A068513 from itertools import islice %o A068513 from sympy import sqrt_mod_iter %o A068513 def A068513_gen(): # generator of terms %o A068513 a = 120 %o A068513 while True: %o A068513 yield a>>3 %o A068513 b = a+1 %o A068513 for d in sqrt_mod_iter(1,a): %o A068513 if d==1 or d**2-1 == a: %o A068513 d += a %o A068513 if d&1 and d < b: %o A068513 b = d %o A068513 a = b**2-1 %o A068513 A068513_list = list(islice(A068513_gen(),10)) # _Chai Wah Wu_, May 05 2024 %Y A068513 Cf. A068776, A068142. %K A068513 nonn %O A068513 0,1 %A A068513 _Robert G. Wilson v_, Mar 19 2002 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE