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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..31.

Michael Gilleland, Levenshtein Distance

Wikipedia, Levenshtein Distance

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

Cf. A007918, A151799, A171400.

Sequence in context: A085814 A009524 A009794 * A104506 A088138 A186033

Adjacent sequences:  A171399 A171400 A171401 * A171403 A171404 A171405

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

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Last modified May 26 17:16 EDT 2022. Contains 354092 sequences. (Running on oeis4.)