A131544 Least power of 3 having exactly n consecutive 9's in its decimal representation.

2, 34, 35, 276, 1520, 2342, 8882, 32313, 164065, 265693, 1123487, 2421341, 6250773, 9995032, 68353789, 78927182

Offset: 1

Author

Shyam Sunder Gupta, Aug 26 2007

Keywords

• more
• nonn
• base

Comments

No more terms < 10^8. - Bert Dobbelaere, Mar 20 2019

Examples

			a(3)=35 because 3^35 (i.e., 50031545098999707) is the smallest power of 3 to contain a run of 3 consecutive nines in its decimal form.
		

Crossrefs

Cf. A195269, A131552, A131551, A131550, A131549, A131548, A131547, A131546, A131545.

Programs

Mathematica

a = ""; Do[ a = StringJoin[a, "9"]; b = StringJoin[a, "9"]; k = 1; While[ StringPosition[ ToString[3^k], a] == {} || StringPosition[ ToString[3^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

Python

def A131544(n):
    m, s = 1, '9'*n
    for i in range(1,10**9):
        m *= 3
        if s in str(m):
            return i
    return "search limit reached." # Chai Wah Wu, Dec 11 2014

Extensions

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

a(15) from Bert Dobbelaere, Mar 04 2019

a(16) from Bert Dobbelaere, Mar 20 2019