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

0,9

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.

Links

R. Zumkeller, Table of n, a(n) for n = 0..2500

Michael Gilleland, Levenshtein Distance

Wikipedia, Levenshtein Distance

Formula

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

Example

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.

Crossrefs

Cf. A007088, A007920.

Sequence in context: A204459 A035155 A090584 * A271592 A357187 A128409

Adjacent sequences: A171397 A171398 A171399 * A171401 A171402 A171403

Keyword

base,nonn

Author

Reinhard Zumkeller, Dec 08 2009

Status

approved