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

Author

Franz Vrabec, Oct 21 2014

Keywords

• nonn

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).

Examples

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

Links

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

Crossrefs

Cf. A000045, A066853.

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

Programs

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)Jinyuan Wang, Mar 20 2020

Formula

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

Extensions

More terms from Jinyuan Wang, Mar 20 2020