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

0,2

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A100292 A078325 A059591 * A303372 A159547 A002522

Adjacent sequences: A082604 A082605 A082606 * A082608 A082609 A082610

Keyword

nonn

Author

Amarnath Murthy, Apr 28 2003

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

Status

approved