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
Links
- Robert Israel, Table of n, a(n) for n = 0..10000
Programs
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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
Comments