A071546 Smallest integer > 1 of the form (k^2+1)/(n^2+1).

5, 2, 5, 10, 17, 26, 37, 5, 65, 82, 101, 2, 13, 170, 197, 226, 61, 10, 325, 362, 5, 61, 13, 530, 577, 626, 41, 149, 785, 65, 73, 17, 149, 146, 1157, 1226, 41, 74, 1445, 1522, 1601, 317, 397, 373, 1937, 221, 97, 74, 2305, 26, 2501, 130, 493, 2810, 5, 3026, 29

Offset

1,1

Comments

a(n) <= n^2 - 2*n + 2 for n > 1, with equality for n in A071557. - Robert Israel, Jan 21 2026

Links

Robert Israel, Table of n, a(n) for n = 1..10000 (first 1000 terms from Vincenzo Librandi)

Formula

a(n) = (A065876(n)^2+1)/(n^2+1).

Maple

f:= proc(n) local S, k;
      S:=map(rhs@op, {msolve(k^2+1, n^2+1)}) minus {n};
      (min(S)^2+1)/(n^2+1)
end proc:
f(1):= 5:
map(f, [$1..100]); # Robert Israel, Jan 21 2026

Mathematica

Table[s=n+1; While[Mod[s^2+1, n^2+1]!=0, s++]; (s^2+1)/(n^2+1), {n, 1, 70}] (* Vincenzo Librandi, Jan 21 2026 *)

Prog

(PARI) for(n=1, 70, s=n+1; while((s^2+1)%(n^2+1)>0, s++); print1((s^2+1)/(n^2+1), ", "))
(Magma) L := []; for n in [1..70] do s := n + 1; while (s^2 + 1) mod (n^2 + 1) ne 0 do s +:= 1; end while; Append(~L, (s^2 + 1) div (n^2 + 1)); end for; L; // Vincenzo Librandi, Jan 21 2026

Crossrefs

Cf. A065876, A071557.

Sequence in context: A236184 A201530 A085997 * A378873 A154649 A100040

Adjacent sequences: A071543 A071544 A071545 * A071547 A071548 A071549

Keyword

easy,nonn,look

Author

Benoit Cloitre, May 30 2002

Status

approved