A018856 2^a(n) is the smallest power of 2 beginning with n.

0, 1, 5, 2, 9, 6, 46, 3, 53, 10, 50, 7, 17, 47, 77, 4, 34, 54, 84, 11, 31, 51, 61, 81, 8, 18, 38, 48, 68, 78, 98, 5, 25, 35, 45, 55, 75, 85, 95, 12, 22, 32, 42, 145, 52, 62, 72, 82, 92, 102, 9, 19, 29, 39, 142, 49, 59, 162, 69, 79, 89, 192, 99, 6, 16, 119, 26

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

References

• A. M. Yaglom and I. M. Yaglom, Challenging Mathematical Problems With Elementary Solutions, Vol. 1, pp. 29, 199-200, Prob. 91a, Dover, NY, 1987.

Links

• Daniel Mondot, Table of n, a(n) for n = 1..32699

Crossrefs

Cf. A018802.

Cf. A100129 (a(n) = n).

Cf. A030000, A000079.

Programs

Haskell

import Data.List (isPrefixOf, findIndex)
import Data.Maybe (fromJust)
a018856 n =
   fromJust $ findIndex (show n `isPrefixOf`) $ map show a000079_list
-- Reinhard Zumkeller, Aug 04 2011

Mathematica

f[n_] := Block[{k = 1, m = Floor[ Log[10, n]]}, While[ Log[10, 2^k] < Floor[ Log[10, n]], k++ ]; While[ Quotient[2^k, 10^(Floor[k*Log[10, 2]] - m)] != n, k++ ]; k]; f[1] = 0;; Array[f, 73] (* Robert G. Wilson v, Jun 02 2009 *)

Python

from itertools import count
def aupton(terms):
    adict, pow2 = dict(), 1
    for i in count(0):
        s = str(pow2)
        for j in range(len(s)):
            t = int(s[:j+1])
            if t > terms:
                break
            if t not in adict:
                adict[t] = i
        if len(adict) == terms:
            return [adict[i+1] for i in range(terms)]
        pow2 *= 2
print(aupton(67)) # Michael S. Branicky, Apr 08 2023