A131536 Exponent of 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
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.
Programs
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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} ] -
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
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