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A051883 a(n) is the smallest number such that the concatenation of a(1)a(2)a(3)...a(n) is divisible by n. 13
1, 0, 2, 0, 0, 0, 5, 6, 4, 0, 5, 16, 2, 4, 0, 0, 14, 4, 9, 20, 16, 26, 13, 6, 25, 22, 34, 4, 14, 0, 17, 28, 42, 22, 20, 24, 31, 44, 36, 0, 15, 24, 2, 8, 20, 36, 8, 16, 32, 50, 35, 6, 47, 58, 40, 16, 4, 26, 12, 40, 51, 52, 38, 4, 5, 12, 74, 56, 2, 20, 11, 68, 44, 58, 75, 24, 7, 38, 87, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
REFERENCES
A. Murthy, Exploring some new ideas on Smarandache type sets, functions and sequences, Smarandache Notions Journal Vol. 11, N 1-2-3 Spring 2000
LINKS
EXAMPLE
For example the third term is 2 because 102 is divisible by 3.
MATHEMATICA
nxt[{n_, c_, a_}]:=Module[{k=0}, While[!Divisible[FromDigits[Flatten[ Join[ IntegerDigits[ c], IntegerDigits[ k]]]], n+1], k++]; {n+1, FromDigits[ Flatten[ Join[IntegerDigits[c], IntegerDigits[k]]]], k}]; NestList[nxt, {1, 1, 1}, 80][[All, 3]] (* Harvey P. Dale, Jul 17 2020 *)
PROG
(Haskell)
import Data.List (findIndex)
import Data.Maybe (fromJust)
a051883 n = a051883_list !! (n-1)
a051883_list = 1 : f 2 "1" where
f :: Integer -> String -> [Int]
f x zs = y : f (x + 1) (zs ++ show y) where
y = fromJust $ findIndex
((== 0) . (`mod` x) . read . (zs ++)) $ map show [0..]
-- Reinhard Zumkeller, May 26 2013
(Python)
from itertools import count, islice
def agen():
b, an = 1, 1
for n in count(2):
yield an
b, pow10 = b*10, 10
r, an = b%n, 0
if r == 0: continue
for d in count(1):
an = (n - r)
while an < pow10//10: an += n
if an < pow10: break
b, pow10 = b*10, pow10*10
r = b%n
b += an
print(list(islice(agen(), 80))) # Michael S. Branicky, Nov 07 2022
CROSSREFS
See A082399 for another version.
Cf. A336399.
Sequence in context: A113044 A333792 A082399 * A132792 A136572 A339016
KEYWORD
nonn,easy,nice,base
AUTHOR
Felice Russo, Dec 15 1999
EXTENSIONS
Expanded and corrected from the Murthy paper.
More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999
Further terms from David Wasserman, Mar 05 2002
STATUS
approved

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)