A298607 Powers of 2 with the digit '0' in their decimal expansion.

1024, 2048, 4096, 131072, 1048576, 2097152, 4194304, 8388608, 67108864, 536870912, 1073741824, 274877906944, 1099511627776, 2199023255552, 4398046511104, 8796093022208, 17592186044416, 35184372088832, 70368744177664, 140737488355328, 281474976710656, 1125899906842624

Offset: 1

Author

Alonso del Arte, Jan 22 2018

Keywords

• nonn
• base

Comments

The complement, A238938, is conjectured to be finite. Furthermore, Khovanova (see link) believes 2^86 = 77371252455336267181195264 is the largest power of 2 not in this sequence.

Examples

			2^12 = 4096 contains one 0 in its decimal representation, hence 4096 is in the sequence.
2^13 = 8192 contains no 0's and is thus not in the sequence.
		

Links

• Tanya Khovanova, "86 Conjecture", Tanya Khovanova's Math Blog, February 15, 2011.

Crossrefs

Cf. A007377, A027870.

Programs

Mathematica

Select[2^Range[0, 63], DigitCount[#, 10, 0] > 0 &]

PARI

lista(nn) = {for (n=0, nn, if (vecsearch(Set(digits(p=2^n)), 0), print1(p, ", ")););} \\ Michel Marcus, Mar 05 2018