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

0,2

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.

Links

Table of n, a(n) for n=0..14.

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

Example

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.

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} ]

Crossrefs

Cf. A006889.

Sequence in context: A050690 A079561 A328326 * A372026 A063296 A372027

Adjacent sequences: A131540 A131541 A131542 * A131544 A131545 A131546

Keyword

more,nonn,base

Author

Shyam Sunder Gupta, Aug 26 2007

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

Status

approved