A064362 Numbers k such that no Lucas number is a multiple of k.

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

Offset: 1

Author

Naohiro Nomoto, Oct 15 2001

Keywords

• easy
• nonn

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

• T. D. Noe, Table of n, a(n) for n = 1..1000
• B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614, 2014 and J. Int. Seq. 17 (2014) # 14.8.5

Crossrefs

Complement of A065156.

Cf. A000032, A124378.

Programs

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[ # ]& ]

Extensions

More terms from Dean Hickerson, Oct 18 2001