This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A228188 #20 Jul 26 2022 01:35:53 %S A228188 10,300,195000,43950000,4106400000,396606000000,25271610000000, %T A228188 83084100000000,22661209000000000,1596879960000000000, %U A228188 3344565630000000000000,3344565630000000000000,3344565630000000000000,1795096118003100000000000000,33778738696128000000000000000 %N A228188 Smallest triangular number divisible by 10^n. %H A228188 Chai Wah Wu, <a href="/A228188/b228188.txt">Table of n, a(n) for n = 1..501</a> %F A228188 a(n) = A228191(n)*(A228191(n)+1)/2. - _Chai Wah Wu_, Jul 25 2022 %e A228188 a(2)=300 because 300 is the smallest triangular number divisible by 10^2. %t A228188 sol[k_, u_] := Block[{x}, Min[x /. List@ToRules[Reduce[Mod[x + u, 2*2^k] == 0 && Mod[x + 1 - u, 5^k] == 0 && x > 0, {x}, Integers] /. C[1] -> 0]]]; a[n_] := Min[sol[n, 0], sol[n, 1]]; p = a /@ Range[15]; p*(p+1)/2 %o A228188 (Python) %o A228188 from sympy.ntheory.modular import crt %o A228188 def A228188(n): return (k:=int(min(crt(m:=(1<<(n+1),5**n),(0,-1))[0], crt(m,(-1,0))[0])))*(k+1)>>1 # _Chai Wah Wu_, Jul 25 2022 %Y A228188 Cf. A000217, A228191. %K A228188 nonn,base %O A228188 1,1 %A A228188 _Shyam Sunder Gupta_, Aug 15 2013