A117971 One-based position of the first 2 from the least significant digit in the ternary expansion of 2^n, or 0 if there are no 2's present.

0, 1, 0, 1, 2, 1, 4, 1, 0, 1, 2, 1, 3, 1, 3, 1, 2, 1, 5, 1, 8, 1, 2, 1, 11, 1, 11, 1, 2, 1, 3, 1, 3, 1, 2, 1, 4, 1, 4, 1, 2, 1, 5, 1, 4, 1, 2, 1, 3, 1, 3, 1, 2, 1, 6, 1, 8, 1, 2, 1, 4, 1, 7, 1, 2, 1, 3, 1, 3, 1, 2, 1, 12, 1, 7, 1, 2, 1, 6, 1, 10, 1, 2, 1, 3, 1, 3, 1, 2, 1, 4, 1, 4, 1, 2, 1, 6, 1, 4, 1, 2, 1, 3, 1

Offset

0,5

Comments

a(0), a(2) and a(8) are the conjectured to be the only terms equal to 0.

Links

Antti Karttunen, Table of n, a(n) for n = 0..16384

Eric Weisstein's World of Mathematics, Ternary

Example

For n=0, 2^0 = 1 is also "1" in base-3, thus there are no 2-digits present, and therefore a(0) = 0.
For n=4, 2^4 = 16, which in base-3 is "121" as 1*(3^2) + 2*3 + 1 = 16, so the rightmost 2 occurs at two steps from the end, therefore a(4) = 2.
For n=5, 2^5 = 32, which in base-3 is "1012" as 1*(3^3) + 1*3 + 2*1 = 32, so the rightmost 2 occurs as the least significant digit (which is the position 1), therefore a(5) = 1.

Mathematica

pf2[n_]:=Module[{p=Position[Reverse[IntegerDigits[2^n, 3]], 2, {1}, 1]}, If[p=={}, 0, p]]; Flatten[Array[pf2, 110]] (* Harvey P. Dale, Nov 30 2013 *)

Prog

(PARI) A117971(n) = { my(n=(2^n), i=1); while(n, if(2==(n%3), return(i)); i++; n \= 3); (0); }; \\ Antti Karttunen, Mar 30 2021

Crossrefs

Cf. A004642 (ternary expansion of 2^n), A007089. See also A117970.

Sequence in context: A140505 A295881 A371890 * A353606 A220420 A190616

Adjacent sequences: A117968 A117969 A117970 * A117972 A117973 A117974

Keyword

nonn,base

Author

Eric W. Weisstein, Apr 06 2006

Extensions

Edited by Charles R Greathouse IV, Aug 05 2010

Term a(0) = 0 prepended, examples added and the definition clarified by Antti Karttunen, Mar 30 2021

Status

approved