OFFSET
1,2
REFERENCES
R. L. Graham, D. E. Knuth and O. Patashnick, "Concrete Mathematics", second edition, Addison Wesley, 1994, ex. 6.85, p. 318, p. 562.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
B. Avila and Y. Chen, On moduli for which the Lucas numbers contain a complete residue system, Fibonacci Quarterly, 51 (2013), 151-152.
S. A. Burr, On moduli for which the Fibonacci numbers contain a complete system of residues, Fibonacci Quarterly, 9 (1971), 497-504.
Cheng Lien Lang and Mong Lung Lang, Fibonacci system and residue completeness, arXiv:1304.2892 [math.NT], 2013.
FORMULA
Consists of the integers of the forms 5^k, 2*5^k, 4*5^k, 3^j*5^k, 6*5^k, 7*5^k and 14*5^k [see Concrete Mathematics].
EXAMPLE
Fibonacci numbers (A000045) are 0,1,1,2,3,5,8,... and their residues mod 5 are 0,1,1,2,3,0,3,3,4,...; i.e., all possible remainders mod 5 occur in the Fibonacci sequence mod 5, so 5 is in the sequence. This is not true for n=8, so 8 is not in the sequence.
MATHEMATICA
Select[Range[10^4], MatchQ[FactorInteger[#], {{1, 1}}|{{2, 1}}|{{2, 2}}| {{3, _}}|{{2, 1}, {3, 1}}|{{7, 1}}|{{2, 1}, {7, 1}}|{{5, _}}|{{2, 1}, {5, _}}|{{2, 2}, {5, _}}|{{3, _}, {5, _}}|{{2, 1}, {3, 1}, {5, _}}|{{5, _}, {7, 1}}|{{2, 1}, {5, _}, {7, 1}}]&] (* Jean-François Alcover, Sep 01 2018 *)
PROG
(PARI) is(n)=n/=5^valuation(n, 5); n==3^valuation(n, 3) || setsearch([2, 4, 6, 7, 14], n) \\ Charles R Greathouse IV, Apr 23 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Feb 01 2003
EXTENSIONS
Corrected by Ron Knott, Jan 05 2005
Entry revised by N. J. A. Sloane, Nov 28 2006, following a suggestion from Martin Fuller
STATUS
approved