The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A060035 Least m >= 0 such that 2^m has n 2's in its base-3 expansion. 0
 0, 1, 3, 12, 9, 16, 15, 19, 27, 30, 44, 40, 55, 52, 65, 60, 51, 75, 73, 80, 86, 82, 81, 77, 98, 85, 95, 79, 118, 141, 162, 107, 129, 105, 158, 145, 155, 143, 138, 152, 203, 176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Previous name was: First power of 2 which has n 2's in its base 3 expansion, or -1 if no such power exists. "Paul Erdős conjectured that for n > 8, 2^n is not a sum of distinct powers of 3. In terms of digits, this states that powers of 2 for n > 8 must always contain a '2' in their base 3 expansion." The value of a(42) is conjectured to be -1 because no power of 2 up to 2^10^7 has exactly 42 2's. After a(42), that is unknown, the sequence goes on 171, 142, 167, 197, 168, 216, 229, 193, 232, 236, 248, 226, 230, 224, 228, 303, 244, ... REFERENCES Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, page 20. LINKS Table of n, a(n) for n=0..41. Brian Hayes, Third Base EXAMPLE a(0) = 0 because 2^0 in base 3 is {1} which has no terms equaling 2. a(6) = 15 because 2^15 in base 3 is {1, 1, 2, 2, 2, 2, 1, 1, 2, 2} which has 6 terms equaling 2. MAPLE for m from 0 to 1000 do r:= numboccur(2, convert(2^m, base, 3)); if not assigned(A[r]) then A[r]:= m fi; od: seq(A[i], i=0..41); # Robert Israel, Dec 08 2015 MATHEMATICA a[n_] := For[k=0, True, k++, If[Count[IntegerDigits[2^k, 3], 2]==n, Return[k]]]; Table[a[n], {n, 0, 41}] (* goes into infinite loop for n > 41 *) a[n_] := -1; Do[m = Count[IntegerDigits[2^(n), 3], 2]; If[a[m] == -1, a[m] = n], {n, 0, 1000}]; Table[a[n], {n, 0, 59}] {* L. Edson Jeffery, Dec 08 2015 *) PROG (PARI) isok(n, k) = {d = digits(2^k, 3); sum(i=1, #d, d[i]==2) == n; } a(n) = {k = 0; while(! isok(n, k), k++); k; } \\ Michel Marcus, Dec 08 2015 CROSSREFS Sequence in context: A070706 A239932 A114237 * A165988 A298028 A215842 Adjacent sequences: A060032 A060033 A060034 * A060036 A060037 A060038 KEYWORD nonn,base,more AUTHOR Robert G. Wilson v, Mar 17 2001 EXTENSIONS Corrected and extended by Sascha Kurz, Jan 31 2003 Zero prepended to sequence by L. Edson Jeffery, Dec 08 2015 New name from L. Edson Jeffery, Dec 08 2015 a(42) = -1 and following terms removed from data by Michel Marcus, Dec 09 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 18 15:59 EDT 2024. Contains 372664 sequences. (Running on oeis4.)