cp's OEIS Frontend

A081806 Least positive number that can be written using prime factors of n (with repetition) and the operations add and subtract.

%I A081806 #7 Sep 14 2013 17:42:34
%S A081806 2,3,4,5,1,7,2,6,3,11,1,13,5,2,4,17,2,19,1,4,9,23,1,10,11,3,3,29,4,31,
%T A081806 2,8,15,2,2,37,17,10,1,41,2,43,7,1,21,47,1,14,2,14,9,53,1,6,1,16,27,
%U A081806 59,2,61,29,1,4,8,6,67,13,20,4,71,2,73,35,3,15,4,8,79,1,6,39,83,4,12,41,26,5
%N A081806 Least positive number that can be written using prime factors of n (with repetition) and the operations add and subtract.
%C A081806 a(n) <= A001414(n); a(n)=A001414(n)=n iff n is prime.
%H A081806 Donovan Johnson, <a href="/A081806/b081806.txt">Table of n, a(n) for n = 2..1000</a>
%e A081806 24=2*2*2*3 -> a(24) = 2-2-2+3 = 1;
%e A081806 30=2*3*5 -> a(30) = 2-3+5 = 4, as -2-3-5<1, -2-3+5<1, -2+3-5<1, -2+3+5>4, 2-3-5<1, 2+3-5<1 and 2+3+5>4.
%o A081806 (PARI) v=vector(9); for(n=2, 1000, c=0; f=factorint(n); for(j=1, omega(n), for(h=1, f[j,2], c++; v[c]=f[j,1])); nn=997; for(j=0, 2^c-1, s=0; for(h=0, c-1, if(bittest(j,h)==0, s=s-v[h+1], s=s+v[h+1])); if(s>0, if(s<nn, nn=s))); write("b081806.txt", n " " nn)) /* _Donovan Johnson_, Sep 14 2013 */
%Y A081806 Cf. A082729, A001222.
%K A081806 nonn
%O A081806 2,1
%A A081806 _Reinhard Zumkeller_, Apr 10 2003