A259092 Smallest k such that 2^k contains three adjacent copies of n in its decimal expansion.

242, 42, 43, 83, 44, 41, 157, 24, 39, 50, 949, 1841, 3661, 1798, 1701, 1161, 1806, 391, 1890, 2053, 950, 1164, 2354, 1807, 3816, 1800, 1799, 818, 1702, 2115, 904, 1798, 1807, 2270, 392, 1699, 3022, 394, 2054, 1758, 1804, 2300, 2720, 2403, 3396, 1133, 1808, 3820

Offset: 0

Author

N. J. A. Sloane, Jun 18 2015

Keywords

• nonn
• base

Comments

The multi-digit generalization of A171242. - R. J. Mathar, Jul 06 2015

Examples

			2^242 = 7067388259113537318333190002971674063309935587502475832486424805170479104 contains three adjacent 0's.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..1000
• Popular Computing (Calabasas, CA), Two Tables, Vol. 1, (No. 9, Dec 1973), page PC9-16.

Crossrefs

Cf. A006889, A131535, A131536, A259089, A063565, A259091.

Programs

Mathematica

Table[k = 0; While[! SequenceCount[IntegerDigits[2^k], Flatten[ConstantArray[IntegerDigits[n], 3]]] > 0, k++]; k, {n, 0, 50}] (* Robert Price, May 17 2019 *)

Python

def A259092(n):
    s, k, k2 = str(n)*3, 0, 1
    while True:
        if s in str(k2):
            return k
        k += 1
        k2 *= 2 # Chai Wah Wu, Jun 18 2015

Extensions

More terms from Chai Wah Wu, Jun 18 2015