A051883 a(n) is the smallest number such that the concatenation of a(1)a(2)a(3)...a(n) is divisible by n.

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

Offset: 1

Author

Felice Russo, Dec 15 1999

Keywords

• nonn
• easy
• nice
• base

Examples

			For example the third term is 2 because 102 is divisible by 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

• Paul Tek, Table of n, a(n) for n = 1..10000

Crossrefs

See A082399 for another version.

Cf. A336399.

Programs

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

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 *)

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

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