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A228191
a(n) is the smallest number m such that the m-th triangular number ends in n zeros.
2
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
Sequence in context: A249028 A216092 A174245 * A012989 A347480 A058171
KEYWORD
nonn,base
AUTHOR
Shyam Sunder Gupta, Aug 15 2013
EXTENSIONS
a(10)-a(20) from Giovanni Resta, Aug 15 2013
STATUS
approved