A082607 a(0)=1; for n > 0, a(n) = least k not included earlier such that k*a(n-1) - 1 is a square.

1, 2, 5, 10, 17, 26, 37, 50, 65, 34, 13, 25, 41, 61, 85, 113, 145, 122, 101, 82, 293, 634, 1105, 53, 109, 185, 74, 149, 250, 377, 205, 146, 97, 58, 29, 73, 137, 221, 181, 650, 541, 442, 353, 274, 953, 2042, 3541, 5450, 409, 173, 370, 289, 218, 157, 106, 337, 698

Offset: 0

Author

Amarnath Murthy, Apr 28 2003

Keywords

• nonn
• changed

Comments

Conjecture: this is a permutation of A008784. - Robert Israel, Aug 25 2025

Links

• Robert Israel, Table of n, a(n) for n = 0..10000

Crossrefs

Contained in A008784. Cf. A082608, A082609, A082610, A082611, A082612.

Programs

Maple

N:= 10000: # for terms before the first term > N
Cands:= select(t -> numtheory:-quadres(-1,t) = 1, [$2..N]): nc:= nops(Cands):
R:= 1: r:= 1:
do
  found:= false;
  for i from 1 to nc do
    if issqr(r*Cands[i]-1) then
       found:= true;
       r:= Cands[i];
       R:= R,r;
       Cands:= subsop(i=NULL,Cands);
       nc:= nc-1;
       break
    fi
  od;
  if not found then break fi
od:
R; # Robert Israel, Aug 25 2025

Mathematica

l = {1}; Do[k = 1; While[MemberQ[l, k] || !IntegerQ[Sqrt[k*Last[l]-1]], k++ ]; AppendTo[l, k], {n, 50}]; l (* Ryan Propper, Jun 13 2006 *)

PARI

a=[1];print1(1",");for(n=2,100,k=1;f=1;while(f,if(issquare(k*a[n-1]-1),f=0;for(i=1,n-1,if(a[i]==k,f=1)));k++);a=concat(a,k-1);print1(k-1",")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007

Extensions

Corrected and extended by Ryan Propper, Jun 13 2006

Definition corrected by R. J. Mathar, Nov 12 2006

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007