A253638 Number of zeros in the decimal expansion of 5^n.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 0, 1, 2, 0, 3, 3, 2, 2, 3, 3, 4, 1, 1, 1, 4, 7, 4, 4, 5, 4, 3, 4, 6, 6, 3, 5, 2, 2, 0, 3, 4, 5, 6, 7, 8, 6, 6, 5, 7, 8, 8, 6, 8, 4, 3, 3, 6, 5, 4, 4, 8, 7, 4, 4, 3, 1, 4, 6, 4, 4, 6, 5, 6, 7, 6, 4, 4, 4, 6, 9, 12, 8, 5, 9, 7, 6, 4, 2, 9, 8, 5, 5, 3, 4, 6, 6, 9, 14, 12, 12, 12, 12, 13

Offset: 0

Author

Zak Seidov, Jan 07 2015

Keywords

• nonn
• base

Comments

Probably a(58) is the last 0 term.

Examples

			5^57 = 6938893903907228377647697925567626953125, 2 zeros hence a(57) = 2,
5^58 = 34694469519536141888238489627838134765625, no zeros hence a(58) = 0,
5^59 = 173472347597680709441192448139190673828125, 3 zeros hence a(59) = 3.
		

Links

• Zak Seidov, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A008839 (no zeros in 5^n), A055641 (number of zeros for n), A000351 (5^n).

Programs

Mathematica

Table[Count[IntegerDigits[5^n],0],{n,0,200}]

PARI

a(n) = my(d = digits(5^n)); sum(i=1, #d, d[i] == 0); \\ Michel Marcus, Jan 15 2015

Formula

a(n) = A055641(A000351(n)). - Michel Marcus, Jan 15 2015