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

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, 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, 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

Offset

2,1

Comments

a(n) <= A001414(n); a(n)=A001414(n)=n iff n is prime.

Links

Donovan Johnson, Table of n, a(n) for n = 2..1000

Example

24=2*2*2*3 -> a(24) = 2-2-2+3 = 1;
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.

Prog

(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 */

Crossrefs

Cf. A082729, A001222.

Sequence in context: A334945 A273825 A082299 * A059806 A332425 A286594

Adjacent sequences: A081803 A081804 A081805 * A081807 A081808 A081809

Keyword

nonn

Author

Reinhard Zumkeller, Apr 10 2003

Status

approved