A171400 Minimal number of editing steps (delete, insert or substitute) to transform the binary representation of n into that of A007918(n), the least prime not less than n.

1, 1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 3, 3, 1, 0, 1, 0, 2, 1, 1, 0, 2, 1, 2, 2, 1, 0, 1, 0, 2, 1, 2, 2, 1, 0, 3, 3, 1, 0, 1, 0, 2, 1, 1, 0, 2, 1, 2, 2, 1, 0, 2, 2, 2, 1, 1, 0, 1, 0, 5, 4, 2, 1, 1, 0, 2, 1, 1, 0, 1, 0, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 3, 3, 1, 0, 4, 4, 4, 4, 5, 5, 1, 0, 2, 2, 1, 0, 1, 0, 2

Offset: 0

Author

Reinhard Zumkeller, Dec 08 2009

Keywords

• base
• nonn

Comments

Delete steps are not necessary;

a(n) = 0 iff n is prime: a(A000040(n))=0;

a(A171401(n)) = 1;

A171402 gives smallest numbers m such that a(m)=n: a(A171402(n))=n.

Examples

			n=14, A007918(14)=17: 14==1110->1100->1100->10001==17, 2 subst and 1 ins: a(14)=3;
n=15, A007918(15)=17: 15==1111->1011->1001->10001==17, 2 subst and 1 ins: a(15)=3;
n=16, A007918(16)=17: 16==10000->10001==17, 1 subst: a(16)=1, A171401(8)=16;
n=17, A007918(17)=17: no editing step: a(17)=0;
n=18, A007918(18)=19: 18==10010->10011==19, 1 subst: a(18)=1, A171401(9)=18.
		

Links

• R. Zumkeller, Table of n, a(n) for n = 0..2500
• Michael Gilleland, Levenshtein Distance
• Wikipedia, Levenshtein Distance

Crossrefs

Cf. A007088, A007920.

Formula

a(n) = BinaryLevenshteinDistance(n, A007918(n)).