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

1,1

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.

Links

Table of n, a(n) for n=1..22.

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A007377, A027870.

Sequence in context: A046314 A221260 A223065 * A366391 A195093 A258734

Adjacent sequences: A298604 A298605 A298606 * A298608 A298609 A298610

Keyword

nonn,base

Author

Alonso del Arte, Jan 22 2018

Status

approved