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

1,3

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

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 * A376202 A132792 A136572

Adjacent sequences: A051880 A051881 A051882 * A051884 A051885 A051886

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