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

Author

Derek Orr, Feb 27 2014

Keywords

• nonn
• base
• fini
• full

Examples

			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).
		

Crossrefs

Cf. A238448, A215727.

Programs

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

Extensions

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