A137519 a(1)=1. a(2)=2. For n>=3, a(n) = the smallest integer > a(n-1) that is coprime to (a(n-1)+1)*(a(n-2)+1).

1, 2, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 39, 41, 43, 47, 49, 53, 59, 61, 67, 69, 71, 73, 77, 79, 83, 89, 97, 101, 103, 107, 109, 113, 119, 121, 127, 129, 131, 133, 137, 139, 143, 149, 151, 157, 159, 161, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 203

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

N:= 100: # for a(1)..a(N)
A[1]:= 1: A[2]:= 2:
for n from 3 to N do
  t:= (A[n-1]+1)*(A[n-2]+1);
  for k from A[n-1]+1 do
    if igcd(k, t)=1 then
      A[n]:= k;
      break
    fi
  od;
od:
[seq(A[i], i=1..N)]: # Robert Israel, Sep 22 2019

Mathematica

a = {1, 2}; For[n = 3, n < 80, n++, i = a[[ -1]] + 1; While[GCD[(a[[ -1]] + 1)*(a[[ -2]] + 1), i] > 1, i++ ]; AppendTo[a, i]]; a (* Stefan Steinerberger, Apr 26 2008 *)
nxt[{a_, b_}]:=Module[{k=b+1, c=(a+1)(b+1)}, While[!CoprimeQ[k, c], k++]; {b, k}]; NestList[nxt, {1, 2}, 60][[;; , 1]] (* Harvey P. Dale, Jan 09 2026 *)

Crossrefs

Sequence in context: A177512 A118751 A173494 * A045344 A087685 A020619

Adjacent sequences: A137516 A137517 A137518 * A137520 A137521 A137522

Keyword

nonn

Author

Leroy Quet, Apr 24 2008

Extensions

More terms from Stefan Steinerberger, Apr 26 2008

Status

approved