A290151 a(n) is the smallest number larger than 1, coprime to n, and differing from n by at least 2, that has not yet appeared in the sequence.

5, 7, 9, 2, 11, 3, 13, 4, 17, 6, 19, 8, 23, 22, 21, 10, 25, 12, 27, 16, 15, 14, 29, 18, 31, 20, 33, 24, 37, 26, 35, 28, 39, 32, 41, 30, 43, 34, 47, 36, 53, 38, 49, 52, 51, 40, 55, 44, 57, 46, 45, 42, 59, 48, 61, 50, 63, 54, 67, 56, 65, 58, 69, 62, 71, 60, 73, 64, 79, 66, 77, 68, 81, 82, 83, 72, 85, 70, 87, 74, 75, 76, 89, 78, 91, 80, 93, 84, 97, 86, 95, 88, 99, 92, 101

Offset

2,1

Comments

It has been proved that a(n) is its own inverse, i.e., that a(a(n)) = n for all n > 1.

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Robert Israel, Proof that a(n) is its own inverse, Mathematics Stack Exchange

Example

a(2), must be at least 4 to differ by 2, but 4 and 2 share a factor of 2 so a(2) must be 5.
a(3), must be at least 5 but 5 is taken by a(2), so it is at least 6, but 6 shares a factor with 3 so it must be at least 7, 7 satisfies all three requirements thus a(3)=7.

Maple

S:= [$2..1000]:
while S <> {} do
  n:= S[1];
  k:= ListTools:-SelectFirst(t -> S[t] > n+1 and igcd(n, S[t])=1, [$2..nops(S)]);
  if k = NULL then break fi;
  R[n]:= S[k]; R[S[k]]:= n;
  S:= subsop(1=NULL, k=NULL, S);
od:
seq(R[i], i=2..n-1); # Robert Israel, Jul 25 2017

Mathematica

a = {1, 5}; Do[k = 2; While[Nand[CoprimeQ[n, k], ! MemberQ[a, k], Abs[n - k] >= 2], k++]; AppendTo[a, k], {n, 3, 96}]; Rest@ a (* Michael De Vlieger, Jul 21 2017 *)

Prog

(Haskell)
f 1=[]
f n|l<-f$n-1=l++[[i|i<-[2..], gcd i n<2, all(/=i)l, abs(n-i)>1]!!0]
-- defines a function f that when given n will generate the first n terms as a list --

Crossrefs

Sequence in context: A104423 A011347 A296490 * A117031 A068456 A239097

Adjacent sequences: A290148 A290149 A290150 * A290152 A290153 A290154

Keyword

nonn

Author

Eamon Olive, Jul 21 2017

Status

approved