

A249104


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


1



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
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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), 139141.


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[#v1]!=0, listput(v, (v[#v]+v[#v1])%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



