A131536 Least power of 2 having exactly n consecutive 2's in its decimal representation.

0, 1, 51, 43, 692, 314, 2354, 8555, 13326, 81784, 279272, 865356, 1727608, 1727602, 23157022, 63416790

Offset

0,3

Links

Table of n, a(n) for n=0..15.

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

Example

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.

Mathematica

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

Prog

(Python)
def A131536(n):
    s, t, m, k, u = '2'*n, '2'*(n+1), 0, 1, '1'
    while s not in u or t in u:
        m += 1
        k *= 2
        u = str(k)
    return m # Chai Wah Wu, Jan 28 2020

Crossrefs

Cf. A006889, A131535, A259089.

Sequence in context: A033371 A191514 A334339 * A204375 A003912 A039932

Adjacent sequences: A131533 A131534 A131535 * A131537 A131538 A131539

Keyword

more,nonn,base

Author

Shyam Sunder Gupta, Aug 26 2007

Extensions

3 more terms from Sean A. Irvine, Jul 19 2010

a(14) from Lars Blomberg, Jan 24 2013

a(15) from Bert Dobbelaere, Feb 25 2019

a(0) from Chai Wah Wu, Jan 28 2020

Status

approved