A228191 a(n) is the smallest number m such that the m-th triangular number ends in n zeros.

4, 24, 624, 9375, 90624, 890624, 7109375, 12890624, 212890624, 1787109375, 81787109375, 81787109375, 81787109375, 59918212890624, 259918212890624, 3740081787109375, 56259918212890624, 256259918212890624, 7743740081787109375, 7743740081787109375

Offset

1,1

Comments

The numbers are often one less than the equivalent entry in A067270. - R. J. Mathar, Aug 27 2013

Because T(n)-n = T(n-1), the terms of this sequence would always be one less than the corresponding entry in A067270 if that sequence included repetitions with leading zeros. For instance, T(81787109376) ends in ...081787109376, so both 81787109376 and 081787109376 could be included. - Robert Dawson, Aug 31 2018

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1000 (terms 1..100 from Giovanni Resta)

Example

a(2)=24 because 24 is the smallest number such that 24th triangular number i.e. 300 ends in 2 '0's.

Mathematica

a = {}; m = 1; Do[b = n*(n + 1)/2; If[Mod[b, 10^m] == 0, m = m + 1; AppendTo[a, n]], {n, 1, 1000000000}]; a
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]]; a /@ Range[20] (* Giovanni Resta, Aug 15 2013 *)

Prog

(Python)
from sympy.ntheory.modular import crt
def A228191(n): return int(min(crt(m:=(1<<(n+1), 5**n), (0, -1))[0], crt(m, (-1, 0))[0])) # Chai Wah Wu, Jul 25 2022

Crossrefs

Cf. A000217, A228188.

Sequence in context: A249028 A216092 A174245 * A012989 A347480 A058171

Adjacent sequences: A228188 A228189 A228190 * A228192 A228193 A228194

Keyword

nonn,base

Author

Shyam Sunder Gupta, Aug 15 2013

Extensions

a(10)-a(20) from Giovanni Resta, Aug 15 2013

Status

approved