A062926 a(1) = 1; a(n) is the smallest square of the form k*a(n-1) + 1, k > 0, i.e., a(n) == 1 (mod a(n-1)), n > 2.

1, 4, 9, 64, 961, 921600, 10070323201, 8364641212206750916, 1474140440485343846897708136232408225, 18289713383512490535096723656013877275576612770471865834506112296448576

Offset

1,2

Comments

If k is allowed to be 0, the sequence would be 1,1,1... - Chai Wah Wu, Mar 27 2020

Links

Robert Israel, Table of n, a(n) for n = 1..12

Example

a(5) = 961 = 15*64 + 1 where a(4) = 64.

Mathematica

a[1] = 1; a[2] = 4; a[n_] := a[n] = (r = Reduce[k > Sqrt[a[n - 1]] && Mod[k^2, a[n - 1]] == 1, k, Integers] /. C[_] -> c; sel = Select[Table[r, {c, -1, 1}], #1 =!= False & ]; Min[k^2 /. ToRules /@ sel]); Table[a[n], {n, 1, 9}] (* Jean-François Alcover, Jan 12 2012 *)

Crossrefs

Sequence in context: A184877 A055859 A162991 * A069020 A220189 A122956

Adjacent sequences: A062923 A062924 A062925 * A062927 A062928 A062929

Keyword

nonn,nice

Author

Amarnath Murthy, Jul 03 2001

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jul 10 2001

a(7) from Vladeta Jovovic, Jan 17 2004

a(9) from Jean-François Alcover, Jan 12 2012

a(10) from Robert Israel, Sep 18 2016

Status

approved