A053030 Numbers with 2 zeros in Fibonacci numbers mod m.

3, 6, 7, 8, 9, 12, 14, 15, 16, 18, 20, 21, 23, 24, 27, 28, 30, 32, 33, 35, 36, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 51, 52, 54, 55, 56, 57, 60, 63, 64, 66, 67, 68, 69, 70, 72, 75, 77, 78, 80, 81, 82, 83, 84, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 103, 104

Offset

1,1

Comments

m is on this list iff m does not have 1 or 4 zeros in the Fibonacci sequence modulo m.

A001176(a(n)) = A128924(a(n),1) = 2. - Reinhard Zumkeller, Jan 17 2014

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Brennan Benfield and Michelle Manes, The Fibonacci Sequence is Normal Base 10, arXiv:2202.08986 [math.NT], 2022.

M. Renault, Fibonacci sequence modulo m

Prog

(Haskell)
a053030 n = a053030_list !! (n-1)
a053030_list = filter ((== 2) . a001176) [1..]
-- Reinhard Zumkeller, Jan 17 2014

Crossrefs

Let {x(n)} be a sequence defined by x(0) = 0, x(1) = 1, x(n+2) = m*x(n+1) + x(n). Let w(k) be the number of zeros in a fundamental period of {x(n)} modulo k.

| m=1 | m=2 | m=3

-----------------------------+----------+---------+---------

The sequence {x(n)} | A000045 | A000129 | A006190

The sequence {w(k)} | A001176 | A214027 | A322906

Primes p such that w(p) = 1 | A112860* | A309580 | A309586

Primes p such that w(p) = 2 | A053027 | A309581 | A309587

Primes p such that w(p) = 4 | A053028 | A261580 | A309588

Numbers k such that w(k) = 1 | A053031 | A309583 | A309591

Numbers k such that w(k) = 2 | this seq | A309584 | A309592

Numbers k such that w(k) = 4 | A053029 | A309585 | A309593

* and also A053032 U {2}

Sequence in context: A047559 A288742 A113826 * A189822 A051205 A168114

Adjacent sequences: A053027 A053028 A053029 * A053031 A053032 A053033

Keyword

nonn,changed

Author

Henry Bottomley, Feb 23 2000

Status

approved