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

1,3

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

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 *)

Prog

(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
(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

Crossrefs

Cf. A018802.

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

Cf. A030000, A000079.

Sequence in context: A367844 A258503 A180726 * A019093 A329986 A097897

Adjacent sequences: A018853 A018854 A018855 * A018857 A018858 A018859

Keyword

nonn,base

Author

David W. Wilson

Status

approved