A197945 Length of longest prefix of A096095(n) that is also a prefix of A096095(n+1).

1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 2, 1, 2, 4, 4, 6, 2, 6, 11, 8, 10, 22, 16, 33, 30, 34, 47, 57, 81, 86, 108, 112, 173, 200, 232, 303, 382, 465, 558, 656, 857, 1051, 1261, 1579, 1972, 2455, 2922, 3594, 4588, 5532, 6839, 8402, 10267, 12976, 15550

Offset

0,13

Links

Table of n, a(n) for n=0..58.

Example

a(17) = A055642(5161) = 4, as 5161 is the longest common prefix of A096095(17)=5161310711827714 and A096095(18)=51618211410616387511.

Prog

(Haskell)
import Data.List (inits, isPrefixOf)
a197945 n = length $ takeWhile (`isPrefixOf` (show $ a096095 $ n+1)) $
                               tail $ inits $ show $ a096095 n
(Python)
from itertools import islice
from os.path import commonprefix
def dws(s, t): # returns string s ++ t where s and t are digits strings, len(s) <= len(t)
    return "".join(str(int(c)+int(d)) for c, d in zip(s.zfill(len(t)), t))
def agen(): # generator of terms
    s, t = "1", "1"
    while True:
        yield len(commonprefix([s, t]))
        s, t = t, dws(s, t)
print(list(islice(agen(), 59))) # Michael S. Branicky, Nov 08 2025

Crossrefs

Cf. A055642.

Sequence in context: A140715 A330690 A263143 * A374336 A099986 A166478

Adjacent sequences: A197942 A197943 A197944 * A197946 A197947 A197948

Keyword

nonn,base

Author

Reinhard Zumkeller, Oct 19 2011

Status

approved