TOC What language is this?

Question

The given set is 1,2,4,8,  . . . . . 2^n in unary number system which is shown in BOLD below

L = {1,11,1111,11111111, . . . . . . . . }

Is it regular or CFL?

Answer 1

Language is neither regular and nor Cfl.

Answer 2

Clearly, it is not a regular language.

There is no DFA which can represent this language.

Comments

Then what L is this? Kindly tell.

Answer 3

Its neither regular nor cfl, notice number of 1's are growing in exponential manner, which we can't simulate using either dfa or pda.

Comments

If we give the regular expression as 1+ then will it make that regular?

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Yes L = {$1^{+}$} is regular, you can easily draw DFA. But language in your question is not ${1^{+}}$.
This language is  L = {$1^{i}$ | i = $2^{n}$, n>=0} over $\sum$ = {1}.

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Yes, you're right. My BAD it's not 1+