A131543 Exponent of least power of 2 having exactly n consecutive 9's in its decimal representation.

0, 12, 33, 50, 421, 422, 2187, 15554, 42483, 42485, 42486, 1522085, 2662514, 6855863, 6855865

Offset: 0

Author

Shyam Sunder Gupta, Aug 26 2007

Keywords

• more
• nonn
• base

Comments

Similarly to A006889, the least power of 2 to contain at least n consecutive 9's will always contain exactly n consecutive 9's. The previous power of two will contain exactly n-1 consecutive 9's preceded by a 4. - Paul Geneau de Lamarlière, Jul 20 2024

No more terms < 28*10^6.

Examples

			a(3)=50 because 2^50 (i.e. 1125899906842624) is the smallest power of 2 to contain a run of 3 consecutive nines in its decimal form.
		

Links

• Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC9-16.

Crossrefs

Cf. A006889.

Programs

Mathematica

a = ""; Do[ a = StringJoin[a, "9"]; b = StringJoin[a, "9"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

Extensions

a(11) from Sean A. Irvine, May 31 2010

a(12)-a(14) from Lars Blomberg, Jan 24 2013

a(0)=0 prepended by Paul Geneau de Lamarlière, Jul 20 2024