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hungry numbers
The  $n$-th hungry number is the smallest number  $k$  such that in the decimal expansion of  $2^k$  appear the first  $n$  decimal digits of  $\pi=3.141592653589793\dots$.

For example, the first hungry number is 5, since  $2^5=\underline{3}2$, the second is 17, since  $2^{17}=1\underline{31}072$  and the third is 74, since

\[ 2^{74}=188894659\underline{314}78580854784\,. \]

The known hungry numbers are 5, 17, 74, 144, 144, 2003, 2003, 37929, 82810, 161449, 712201, 2401519, 7339199, 33662541.

Pictorial representation of remainders (mod 2, 3, ...,11) frequency. For a table of values and more details click here
remainders of hungry numbers
Useful links OEIS, Sequence A102387
Hungry numbers can also be... (you may click on names or numbers)

aban 17 74 144 abundant 144 82810 alternating 74 amenable 17 144 37929 161449 712201 33662541 arithmetic 17 2003 37929 161449 712201 2401519 7339199 Chen 17 2003 congruent 712201 2401519 7339199 constructible 17 Cunningham 17 Curzon 74 cyclic 17 2003 37929 161449 2401519 de Polignac 161449 deficient 17 74 2003 37929 161449 712201 2401519 7339199 dig.balanced 712201 Duffinian 144 161449 712201 2401519 economical 17 2003 161449 2401519 emirp 17 emirpimes 2401519 equidigital 17 2003 161449 2401519 evil 17 144 2003 37929 161449 712201 2401519 33662541 Fibonacci 144 gapful 712201 2401519 good prime 17 happy 2003 82810 Harshad 144 iban 17 74 144 2003 712201 inconsummate 37929 interprime 144 37929 33662541 Jordan-Polya 144 junction 37929 33662541 katadrome 74 Leyland 17 magnanimous 74 metadrome 17 modest 2003 nialpdrome 74 nude 144 oban 17 odious 74 82810 7339199 panconsummate 144 pernicious 17 74 144 7339199 Perrin 17 Pierpont 17 plaindrome 17 144 power 144 powerful 144 practical 144 prime 17 2003 Proth 17 pseudoperfect 144 82810 self 2401519 semiprime 74 161449 2401519 Sophie Germain 2003 sphenic 37929 712201 7339199 33662541 square 144 strong prime 17 super-d 82810 2401519 truncatable prime 17 twin 17 uban 17 Ulam 161449 712201 wasteful 74 144 37929 82810 712201 7339199 weak prime 2003 Woodall 17 Zuckerman 144 Zumkeller 82810