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

0,1

Comments

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

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.

Example

2^53 = 9007199254740992 contains two adjacent 0's.

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 *)

Prog

(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

Crossrefs

Cf. A006889, A131535, A131536, A259089, A063565, A259092.

Sequence in context: A289237 A319904 A171132 * A104936 A262908 A109648

Adjacent sequences: A259088 A259089 A259090 * A259092 A259093 A259094

Keyword

nonn,base

Author

N. J. A. Sloane, Jun 18 2015

Extensions

More terms from Chai Wah Wu, Jun 18 2015

Status

approved