A081230 a(n) is the Levenshtein distance between n and n^n (where each is treated as a string).

1, 0, 1, 2, 3, 3, 4, 6, 8, 8, 9, 10, 11, 13, 16, 17, 18, 19, 22, 23, 26, 26, 28, 30, 32, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 86, 88, 90, 92, 94, 96, 99, 101, 103, 105, 107, 110, 112, 114, 116, 119, 121, 123, 125

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

M. Gilleland, Levenshtein Distance. [It has been suggested that this algorithm gives incorrect results sometimes. - N. J. A. Sloane]

Example

a(9)=8 since we can transform 9 into 9^9=387420489 by 8 insertions, namely inserting 3,8,7,4,2,0,4 and 8 in front of 9. a(2)=1 since we can transform 2 into 2^2=4 by one substitution, namely 4 for 2.

Maple

a:= n-> StringTools[Levenshtein](""||n, ""||(n^n)):
seq(a(n), n=0..69);  # Alois P. Heinz, Oct 16 2025

Mathematica

levenshtein[s_List, t_List] := Module[{d, n = Length@s, m = Length@t}, Which[s === t, 0, n == 0, m, m == 0, n, s != t, d = Table[0, {m + 1}, {n + 1}]; d[[1, Range[n + 1]]] = Range[0, n]; d[[Range[m + 1], 1]] = Range[0, m]; Do[ d[[j + 1, i + 1]] = Min[d[[j, i + 1]] + 1, d[[j + 1, i]] + 1, d[[j, i]] + If[ s[[i]] === t[[j]], 0, 1]], {j, m}, {i, n}]; d[[ -1, -1]] ]];
f[n_] := levenshtein[IntegerDigits[n], IntegerDigits[n^n]]; Array[f, 69] (* Robert G. Wilson v *)

Prog

(Python)
from Levenshtein import distance as LD
def a(n): return LD(str(n), str(n**n))
print([a(n) for n in range(70)]) # Michael S. Branicky, Oct 16 2025

Crossrefs

Cf. A000312, A081355.

Sequence in context: A253926 A277579 A241447 * A341144 A365831 A036021

Adjacent sequences: A081227 A081228 A081229 * A081231 A081232 A081233

Keyword

nonn,base

Author

Francois Jooste (pin(AT)myway.com), Mar 11 2003

Extensions

Corrected by Robert G. Wilson v, Jan 25 2006

a(0)=1 prepended by Alois P. Heinz, Oct 16 2025

Status

approved