A256285 a(n) = smallest divisor of the concatenation of n+1 and n, that did not occur earlier.

1, 2, 43, 3, 5, 4, 29, 7, 109, 6, 173, 8, 9, 757, 17, 11, 23, 14, 673, 10, 2221, 18, 2423, 631, 15, 47, 257, 12, 13, 313, 359, 28, 3433, 19, 727, 467, 1279, 22, 577, 20, 4241, 26, 1481, 16, 929, 21, 37, 1237, 27, 25, 59, 24, 41, 2777, 39, 1439, 5857, 331, 73

Offset: 1

Author

Eric Angelini and Reinhard Zumkeller, Jun 03 2015

Keywords

• nonn
• base

Comments

Is this a permutation of the integers > 0 ?

From Robert Israel, May 20 2024: (Start)

Yes, this is a permutation of the positive integers.

For any positive integer k, there are arbitrarily large d such that 10^(d-1) > k and GCD(10^d + 1, k) == 1. For such d, there is n such that n == -10^d (10^d + 1)^(-1) (mod k) and 10^d > n >= 10^(d-1), and this implies that the concatenation of n+1 and n, which is 10^d * (n+1) + n, is divisible by k. After all numbers < k have occurred, the next such n must have a(n) = k. (End)

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Éric Angelini, Divisors of the concatenation of n+1 and n, SeqFan list, Jun 03 2015.

Crossrefs

Cf. A027750, A127423, A253253.

Programs

Haskell

import Data.List (insert); import Data.List.Ordered (minus)
a256285 n = a256285_list !! (n-1)
a256285_list = f (tail a127423_list) [] where
   f (x:xs) ds = y : f xs (insert y ds) where
                 y = head (a027750_row x `minus` ds)

Maple

R:= NULL: S:= {}:
for n from 1 to 100 do
  v:=  10^(1+ilog10(n))*(n+1)+n;
  s:= min(numtheory:-divisors(v) minus S);
  R:= R,s;
  S:= S union {s};
od:
R; # Robert Israel, May 20 2024