login
A171402
Smallest number m such that exactly n editing steps (insert or substitute) are necessary to transform the binary representation of m into the least prime not less than m.
1
2, 0, 8, 14, 63, 62, 252, 254, 766, 2040, 4095, 4094, 12286, 32750, 32764, 65534, 262141, 262140, 1048574, 2097150, 7340030, 8388602, 25165820, 33554428, 67108860, 134217696, 268435420, 268435452, 1073741790, 1073741820, 3221225470, 8589934590
OFFSET
0,1
FORMULA
A171400(a(n)) = n.
BinaryLevenshteinDistance(a(n), A007918(a(n))) = n.
For n > 1, A007918(a(n)) must have >= n+1 digits and empirically a(n) >= A151799(A007918(2^(n+1))) + 1 - Michael S. Branicky, Feb 05 2022
PROG
(Python)
from Levenshtein import distance # after pip install python-Levenshtein
from sympy import nextprime
def a(n):
m = 0
while True:
b = bin(m)[2:]
if distance(b, bin(nextprime(m-1))[2:]) == n:
return m
m += 1
print([a(n) for n in range(1, 16)]) # Michael S. Branicky, Feb 05 2022
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Reinhard Zumkeller, Dec 08 2009
EXTENSIONS
a(10)-a(26) from Michael S. Branicky, Feb 05 2022
a(27)-a(29) from Michael S. Branicky, Feb 06 2022
a(30)-a(31) from Michael S. Branicky, Feb 19 2022
STATUS
approved