A249104 Defective numbers: A complete residue system mod a(n) does not exist in the Fibonacci sequence.

8, 11, 12, 13, 16, 17, 18, 19, 21, 22, 23, 24, 26, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87

Offset

1,1

Comments

Every multiple of a member is a member.

Every integer 2^r*m (r>2, m odd) is a member.

Every prime p congruent 1, 9, 11, 13, 17, 19 (mod 20) is a member (see reference).

Links

Table of n, a(n) for n=1..66.

A. P. Shah, Fibonacci Sequence Modulo m, Fibonacci Quarterly, Vol.6, No.2 (1968), 139-141.

Formula

A066853(a(n)) < a(n) in ascending order.

Example

16 is a member because A066853(16) = 11 < 16.

Prog

(PARI) isok(k) = {if(k<8, return(0)); my(v=List([1, 2])); while(v[#v]!=1 || v[#v-1]!=0, listput(v, (v[#v]+v[#v-1])%k)); #Set(v)<k; } \\ Jinyuan Wang, Mar 20 2020

Crossrefs

Cf. A000045, A066853.

Complement of A079002. - Jeppe Stig Nielsen, Dec 11 2017

Sequence in context: A077060 A123939 A134787 * A191887 A122195 A064153

Adjacent sequences: A249101 A249102 A249103 * A249105 A249106 A249107

Keyword

nonn

Author

Franz Vrabec, Oct 21 2014

Extensions

More terms from Jinyuan Wang, Mar 20 2020

Status

approved