A259091 Smallest k such that 2^k contains two adjacent copies of n in its decimal expansion.

53, 40, 43, 25, 18, 16, 46, 24, 19, 33, 378, 313, 170, 374, 361, 359, 64, 34, 507, 151, 348, 246, 314, 284, 349, 314, 261, 151, 385, 166, 156, 364, 65, 219, 371, 359, 503, 148, 155, 352, 349, 308, 247, 255, 192, 387, 165, 149, 171, 150, 210, 155, 209, 101, 505

Offset: 0

Author

N. J. A. Sloane, Jun 18 2015

Keywords

• nonn
• base

Comments

The multi-digit generalization of A171132. - R. J. Mathar, Jul 06 2015

Examples

			2^53 = 9007199254740992 contains two 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, A259092.

Programs

Mathematica

Table[k = 0; While[! SequenceCount[IntegerDigits[2^k], Flatten[ConstantArray[IntegerDigits[n], 2]]] > 0, k++]; k, {n, 0, 100}] (* Robert Price, May 17 2019 *)

Python

def A259091(n):
    s, k, k2 = str(n)*2, 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