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

1,2

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.

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

Prog

(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)

Crossrefs

Cf. A027750, A127423, A253253.

Sequence in context: A273399 A052078 A069544 * A360549 A268467 A236695

Adjacent sequences: A256282 A256283 A256284 * A256286 A256287 A256288

Keyword

nonn,base

Author

Eric Angelini and Reinhard Zumkeller, Jun 03 2015

Status

approved