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.
1, 2, 12, 112, 21, 22, 122, 1122, 11122, 211, 212, 1212, 221, 222, 1222, 11222, 111222, 1111222, 2111, 2112, 12112, 2121, 2122, 12122, 112122, 2211, 2212, 12212, 2221, 2222, 12222, 112222, 1112222, 11112222, 111112222, 21111, 21112, 121112, 21121, 21122
Offset: 1
Examples
a(4) = 112 because 1^3 + 1^2 + 2^1 = 4. 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.
Links
- Giovanni Resta, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
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 *)