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A064362 Numbers n such that no Lucas number is a multiple of n. 5
5, 8, 10, 12, 13, 15, 16, 17, 20, 21, 24, 25, 26, 28, 30, 32, 33, 34, 35, 36, 37, 39, 40, 42, 45, 48, 50, 51, 52, 53, 55, 56, 57, 60, 61, 63, 64, 65, 66, 68, 69, 70, 72, 73, 74, 75, 77, 78, 80, 84, 85, 87, 88, 89, 90, 91, 92, 93, 95, 96, 97, 99, 100, 102, 104 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Any positive multiple of a member of this sequence is also a member. Primitive elements are in A124378. - Franklin T. Adams-Watters, Oct 28 2006
The Mathematica code for testing the number n works by generating the Lucas sequence (mod n) and stopping when either n divides a term of the sequence or the entire sequence (mod n) has been generated. Hence, up to A106291(n) terms need to be computed. - T. D. Noe, Mar 20 2013
REFERENCES
Teruo Nishiyama, Fibonacci numbers, Suuri-Kagaku, No. 285, March 1987, 67-69, (in Japanese).
LINKS
B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614, 2014 and J. Int. Seq. 17 (2014) # 14.8.5
MATHEMATICA
test[ n_ ] := For[ a=1; b=3, True, t=b; b=Mod[ a+b, n ]; a=t, If[ b==0, Return[ True ] ]; If[ a==2&&b==1, Return[ False ] ] ]; Select[ Range[ 110 ], !test[ # ]& ]
CROSSREFS
Complement of A065156.
Sequence in context: A332556 A049195 A172019 * A173298 A248356 A115401
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Oct 15 2001
EXTENSIONS
More terms from Dean Hickerson, Oct 18, 2001
STATUS
approved

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Last modified June 17 15:45 EDT 2024. Contains 373458 sequences. (Running on oeis4.)