A131535 Exponent of least power of 2 having exactly n consecutive 1's in its decimal representation.

1, 0, 40, 42, 313, 485, 1841, 8923, 8554, 81783, 165742, 1371683, 1727601, 9386566, 28190643, 63416789

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)=42 because 2^42(i.e. 4398046511104) is the smallest power of 2 to contain a run of 3 consecutive ones in its decimal form.

Mathematica

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

Prog

(Python)
def A131535(n):
    s, t, m, k, u = '1'*n, '1'*(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, A131536, A259089, A063565, A259091, A259092.

Sequence in context: A111167 A378652 A070980 * A118473 A118635 A097373

Adjacent sequences: A131532 A131533 A131534 * A131536 A131537 A131538

Keyword

more,nonn,base

Author

Shyam Sunder Gupta, Aug 26 2007

Extensions

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

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

a(15) from Bert Dobbelaere, Feb 25 2019

a(0) added and a(1) corrected by Chai Wah Wu, Jan 28 2020

Status

approved