A073853 Indices of zeros in A079777.

0, 5, 9, 12, 24, 45, 60, 65, 179, 764, 1268, 5891, 16135, 29909, 71774, 173310, 200040, 1454560, 2485272, 86430343, 92439810, 115854652, 7208007982, 17016737751, 17589706947, 24531053552, 33113576855, 80692537585, 234365843350, 266484243960, 285357252641, 426388494035, 975986718040, 1505420538689, 43633539697333

Offset: 1

Author

Benoit Cloitre, Sep 02 2002

Keywords

• nonn

Comments

Let b(1) = b(2) = 1, b(k) = (b(k-1) + b(k-2)) mod k; sequence gives n such that b(n) = 0.

A079777(2^31-1) = 1103802855, and A079777(2^31) = 2117709557.

No further terms below k = 5*10^10, at which point, A079777(k-1) = 6059364906669 and A079777(k) = 29451014544130. - Luca Armstrong, Apr 07 2023

Examples

			b(3) = 2 mod 3 = 2; b(4) = (2+1) mod 4 = 3; b(5) = (3+2) mod 5 = 0, hence a(1) = 5.
		

Links

• Zak Seidov, A073853 Four more terms [From _Zak Seidov_, Dec 06 2009]

Crossrefs

A079777(n) = 0.

Programs

Java

class A073853 { public static void main(String [] args) { BigInteger an = BigInteger.ZERO ; BigInteger an1 = BigInteger.ONE ; BigInteger n = new BigInteger("2") ; for( ; ; n = n.add(BigInteger.ONE) ) { BigInteger an2 = an.add(an1).mod(n) ; if ( an2.compareTo(BigInteger.ZERO) == 0 ) System.out.println(n) ; an = an1 ; an1 = an2 ; } } } // R. J. Mathar, Dec 06 2009

Mathematica

a = 0; b = 1; lst = {0}; Do[c = Mod[a + b, n]; If[c == 0, AppendTo[lst, n]; Print@n]; a = b; b = c, {n, 2, 2^31}] (* Robert G. Wilson v *)

Extensions

Corrected and extended by John W. Layman, Jun 11 2003

a(23)-a(26) from Zak Seidov; a(27)-a(28) from John W. Layman; a(29)-a(34) from Charles R Greathouse IV, Dec 09 2009. (These new terms were added by N. J. A. Sloane, Dec 20 2009.)

a(35) from Luca Armstrong, Apr 07 2023