A235869 Least number k such that 3^k begins with exactly n identical digits.

1, 19, 33, 2061, 6563, 17853, 2319050, 2061700, 57587802, 2725111202, 6121395677, 79432391610, 5689239922828, 9667911135850, 253066675679888, 959406299366116, 2267148455007422, 182092146481798583, 1074950828335499452, 3586769629515088106, 72389675081649855753

Offset

1,2

Comments

a(7) > 200000.

The repeating digits that correspond to these data values are {3, 1, 5, 2, 2, 1, 1, 7, 2, 8, 1} respectively.

a(12) > 2 * 10^10 - Hiroaki Yamanouchi, Jul 13 2014

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100

Example

3^19 = 1162261467 begins with two identical digits ('11'). Thus a(2) = 19.

Prog

(Python)
def b(n):
..for k in range(1, 2*10**5):
....st = str(3**k)
....count = 0
....if len(st) >= n:
......for i in range(len(st)):
........if st[i] == st[0]:
..........count += 1
........else:
..........break
......if count == n:
........return k
n = 1
while n < 10:
..print(b(n), end=', ')
..n += 1

Crossrefs

Sequence in context: A223608 A146438 A146571 * A140601 A031206 A214231

Adjacent sequences: A235866 A235867 A235868 * A235870 A235871 A235872

Keyword

nonn,base

Author

Derek Orr, Jun 13 2014

Extensions

a(7)-a(11) from Hiroaki Yamanouchi, Jul 13 2014

a(12)-a(21) from Hiroaki Yamanouchi, May 31 2015

Status

approved