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A051883
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a(n) is the smallest number such that the concatenation of a(1)a(2)a(3)...a(n) is divisible by n.
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13
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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
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OFFSET
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1,3
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REFERENCES
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A. Murthy, Exploring some new ideas on Smarandache type sets, functions and sequences, Smarandache Notions Journal Vol. 11, N 1-2-3 Spring 2000
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LINKS
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EXAMPLE
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For example the third term is 2 because 102 is divisible by 3.
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MATHEMATICA
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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 *)
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PROG
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(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..]
(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
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CROSSREFS
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KEYWORD
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nonn,easy,nice,base
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AUTHOR
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EXTENSIONS
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Expanded and corrected from the Murthy paper.
More terms from Michael Lugo (mlugo(AT)thelabelguy.com), Dec 22 1999
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STATUS
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approved
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