A259089 Least k such that 2^k has at least n consecutive 2's in its decimal representation.

0, 1, 43, 43, 314, 314, 2354, 8555, 13326, 81784, 279272, 865356, 1727602, 1727602

Offset: 0

Author

N. J. A. Sloane, Jun 18 2015

Keywords

• more
• nonn
• base

Examples

			a(3)=43 because 2^43 (i.e. 8796093022208) is the smallest power of 2 to contain a run of 3 consecutive twos 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, A063565, A259091, A259092.

Programs

Mathematica

Table[k = 0; While[! SequenceCount[IntegerDigits[2^k], ConstantArray[2, n]] > 0, k++]; k, {n, 10}] (* Robert Price, May 17 2019 *)

Python

def A259089(n):
    s, k, k2 = '2'*n, 0, 1
    while True:
        if s in str(k2):
            return k
        k += 1
        k2 *= 2 # Chai Wah Wu, Jun 19 2015

Extensions

a(7)-a(13) from Chai Wah Wu, Jun 20 2015

Definition corrected by Manfred Scheucher, Jun 23 2015

a(0) prepended by Chai Wah Wu, Jan 28 2020