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

1,2

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

Links

Table of n, a(n) for n=1..35.

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

Example

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

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 *)

Prog

(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

Crossrefs

A079777(n) = 0.

Sequence in context: A314649 A314650 A220187 * A070370 A277617 A103703

Adjacent sequences: A073850 A073851 A073852 * A073854 A073855 A073856

Keyword

nonn

Author

Benoit Cloitre, Sep 02 2002

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

Status

approved