A131551 Least power of 3 having exactly n consecutive 2's in its decimal representation.

3, 19, 148, 253, 330, 2380, 2124, 30598, 22791, 238582, 107187, 1521134, 10363119, 9995030, 68353787

Offset: 1

Author

Shyam Sunder Gupta, Aug 26 2007

Keywords

• more
• nonn
• base

Examples

			a(3)=148 because 3^148 (i.e. 41109831670569663658300086939077404909608122265524774868353822811305361) is the smallest power of 3 to contain a run of 3 consecutive twos in its decimal form.
		

Crossrefs

Cf. A195269, A131552, A131550, A131549, A131548, A131547, A131546, A131545, A131544.

Programs

Mathematica

a = ""; Do[ a = StringJoin[a, "2"]; b = StringJoin[a, "2"]; k = 1; While[ StringPosition[ ToString[3^k], a] == {} || StringPosition[ ToString[3^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

Python

def a(n):
  k, n2, np2 = 1, '2'*n, '2'*(n+1)
  while True:
    while not n2 in str(3**k): k += 1
    if np2 not in str(3**k): return k
    k += 1
print([a(n) for n in range(1, 8)]) # Michael S. Branicky, Mar 19 2021

Extensions

a(11)-a(14) from Lars Blomberg, Feb 02 2013

a(15) from Bert Dobbelaere, Mar 04 2019