A235860 - OEIS

A235860

Minimal representation (considered minimal in any canonical base b >= 3) of n in a binary system using two distinct digits "1" and "2", not allowing zeros, where a digit d in position p (p = 1,2,3,...,n) represents the value d^p.

%I #38 Dec 09 2014 03:32:53

%S 1,2,12,112,21,22,122,1122,11122,211,212,1212,221,222,1222,11222,

%T 111222,1111222,2111,2112,12112,2121,2122,12122,112122,2211,2212,

%U 12212,2221,2222,12222,112222,1112222,11112222,111112222,21111,21112,121112,21121,21122

%N Minimal representation (considered minimal in any canonical base b >= 3) of n in a binary system using two distinct digits "1" and "2", not allowing zeros, where a digit d in position p (p = 1,2,3,...,n) represents the value d^p.

%H Giovanni Resta, <a href="/A235860/b235860.txt">Table of n, a(n) for n = 1..1000</a>

%e a(4) = 112 because 1^3 + 1^2 + 2^1 = 4.

%e 36(10) in base 10 is represented as 21111 in this base because 2^5 + 1^4 + 1^3 + 1^2 + 1^1 = 36. It could also be represented as 1111112222. The minimal representation, considered in base 10, is chosen.

%t t = Range[1000]*0; Do[d=1+IntegerDigits[k, 2, n]; dd = FromDigits@d; v = Total[ Reverse[d]^ Range[n]]; If[0 < v <= 1000 && (t[[v]] == 0 || dd < t[[v]]), t[[v]] = dd], {n,17}, {k, 0, 2^n-1}]; t (* first 1000 terms, _Giovanni Resta_, Jan 16 2014 *)

%Y Cf. A007931, A236547, A237662, A237816, A237454.

%K nonn,base

%O 1,2

%A _Robin Garcia_, Jan 16 2014