A295562 List of numbers whose middle Fibonomial coefficient (2n,n)_F is prime to 105.

1, 1312, 3256, 3257, 3936, 3937, 4000, 4001, 4032, 38880, 38881, 39000, 39001, 19928280, 19928281, 21975136, 21975137, 21975305, 21975312, 22054032

Offset

1,2

Comments

From Charlie Neder, Mar 04 2019: (Start)

For the middle Fibonomial coefficient (2n,n)_F to be coprime to a prime p, we must have that the integral part of n/A001177(p) has its base-p digits all < p/2 and its fractional part is < 1/2.

Next term > 10^8. (End)

Links

Table of n, a(n) for n=1..20.

Christian Ballot, Divisibility of the middle Lucasnomial coefficient, Fib. Q., 55 (2017), 297-308.

Formula

Numbers k congruent to 0 or 1 modulo 8 such that floor(k/4) is in A005836, k is in A037543, and floor(k/8) is in A037461. - Charlie Neder, Mar 04 2019

Crossrefs

Cf. A003267, A030979.

Cf. A037461, A037543, A005836.

Sequence in context: A205301 A320506 A322834 * A030646 A223612 A223413

Adjacent sequences: A295559 A295560 A295561 * A295563 A295564 A295565

Keyword

nonn,more

Author

N. J. A. Sloane, Nov 28 2017

Extensions

a(10)-a(20) from Charlie Neder, Mar 04 2019

Status

approved