A131540 Exponent of least power of 2 having exactly n consecutive 6's in its decimal representation.

0, 4, 46, 157, 222, 220, 2269, 11019, 18842, 192918, 192916, 271979, 1039316, 7193133, 14060686, 97428976

Offset: 0

Author

Shyam Sunder Gupta, Aug 26 2007

Keywords

• more
• nonn
• base

Examples

			a(3)=157 because 2^157(i.e. 182687704666362864775460604089535377456991567872) is the smallest power of 2 to contain a run of 3 consecutive sixes in its decimal form.
		

Links

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

Crossrefs

Cf. A006889, A131535, A131536, A131537, A131538, A131539, A131541, A131542, A131543.

Programs

Mathematica

a = ""; Do[ a = StringJoin[a, "6"]; b = StringJoin[a, "6"]; k = 1; While[ StringPosition[ ToString[2^k], a] == {} || StringPosition[ ToString[2^k], b] != {}, k++ ]; Print[k], {n, 1, 10} ]

Extensions

Two more terms from Sean A. Irvine, May 31 2010

a(13)-a(14) from Lars Blomberg, Jan 24 2013

a(15) from Bert Dobbelaere, Mar 07 2019

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