A238507 Smallest number m such that 3^m contains a string of n consecutive increasing integers in its decimal representation.

0, 8, 20, 57, 332, 332, 6814, 7926, 16724, 200633

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Example

8 is the smallest exponent such that 3^8 contains two consecutive increasing integers (3^8 = 6561).
20 is the smallest exponent such that 3^20 contains three consecutive increasing integers (3^20 = 3486784401).

Prog

(Python)
def StrInc(x):
..for n in range(10**5):
....count = 0
....i = 0
....string = str(3**n)
....if len(string) == x and x == 1:
......return n
....while i < len(string)-1:
......if int(string[i]) == int(string[i+1])-1:
........count += 1
........i += 1
......else:
........if count >= x-1:
..........return n
........else:
..........count = 0
..........i += 1
....if count >= x-1:
......return n
x = 1
while x < 15:
..print(StrInc(x))
..x += 1

Crossrefs

Cf. A238448, A215727.

Sequence in context: A360222 A212758 A179756 * A101363 A003685 A066011

Adjacent sequences: A238504 A238505 A238506 * A238508 A238509 A238510

Keyword

nonn,base,fini,full

Author

Derek Orr, Feb 27 2014

Extensions

a(8)-a(10) from Giovanni Resta, Mar 02 2014

Status

approved