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

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

1,1

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

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

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.

Cf. A000032, A124378.

Sequence in context: A332556 A049195 A172019 * A173298 A248356 A115401

Adjacent sequences: A064359 A064360 A064361 * A064363 A064364 A064365

Keyword

easy,nonn

Author

Naohiro Nomoto, Oct 15 2001

Extensions

More terms from Dean Hickerson, Oct 18, 2001

Status

approved