A065156 -id:A065156 - cp's OEIS frontend

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

Naohiro Nomoto, Oct 15 2001

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

Teruo Nishiyama, Fibonacci numbers, Suuri-Kagaku, No. 285, March 1987, 67-69, (in Japanese).

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

Complement of A065156.

Cf. A000032, A124378.

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[ # ]& ]

More terms from Dean Hickerson, Oct 18 2001

A124378 Primitive elements of A064362.

Original entry on oeis.org

5, 8, 12, 13, 17, 21, 28, 33, 37, 53, 57, 61, 69, 73, 77, 87, 89, 92, 93, 97, 109, 113, 133, 137, 141, 149, 157, 164, 172, 173, 177, 188, 193, 197, 203, 213, 217, 233, 237, 253, 257, 268, 269, 277, 287, 293, 301, 303, 309, 313, 317, 329, 332, 337, 353, 373, 381

Offset: 1

Franklin T. Adams-Watters, Oct 28 2006

nonn

Numbers n such that no Lucas number is a multiple of n, which are not divisible by any smaller number with that property.

T. D. Noe, Table of n, a(n) for n = 1..1000

Cf. A064362, A065156.

test[n_] := Module[{a, b, t}, {a, b} = {2, 1}; While[t = b; b = Mod[a + b, n]; a = t; ! (b == 0 || {a, b} == {2, 1})]; b == 0]; t = {}; n = 0; While[Length[t] < 1000, n++; If[! MemberQ[Mod[n, t], 0] && ! test[n], AppendTo[t, n]]]; t (* T. D. Noe, Mar 20 2013 *)

A232658 Numbers that are factors of Lucas numbers, whose multiples do not appear in some other Fibonacci-like sequence.

Original entry on oeis.org

11, 18, 19, 22, 29, 31, 38, 41, 44, 46, 47, 54, 58, 59, 62, 71, 76, 79, 82, 94, 101, 107, 116, 118, 121, 123, 124, 129, 131, 139, 142, 151, 158, 161, 162, 166, 179, 181, 191, 199, 201, 202, 209, 211, 214, 229, 236, 239, 241, 242, 246, 249, 251, 258, 262, 263, 271

Offset: 1

Brandon Avila and Tanya Khovanova, Nov 27 2013

nonn

Intersection of A230457 and A065156.

Sequence A230457 from which elements of A064362 are removed.

			Sequence A000285 is the Fibonacci-like sequence starting with 1 and 4. This sequence doesn't contain multiples of 11. On the other hand Lucas numbers contain multiples of 11. Therefore, 11 belongs to this sequence.

B. Avila and T. Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614, 2014 and J. Int. Seq. 17 (2014) # 14.8.5

Cf. A230457, A065156, A064362.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Mathematica

Extensions

A124378 Primitive elements of A064362.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

A232658 Numbers that are factors of Lucas numbers, whose multiples do not appear in some other Fibonacci-like sequence.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs