A298686 -id:A298686

A298687

Numbers i such that Fibonacci(i) is divisible by i+k for k=0..5.

+10
5

13440, 19440, 329400, 600600, 2499840, 3150840, 5590200, 7660800, 69069000, 83980800, 96049800, 98385840, 175472640, 179663400, 237484800, 320498640, 330663600, 375396840, 404351640, 406380240, 429660000, 437940000, 505234800, 574585200, 635980800

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A subsequence of A298686.

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..57

PROG

(Python)

p0 = 0

p1 = 1

for i in range(1, 1000000):

if p1 % i == 0 and p1 % (i+1) == 0 and p1 % (i+2) == 0:

if p1 % (i+3) == 0 and p1 % (i+4) == 0 and p1 % (i+5) == 0: print i

p0, p1 = p1, p0+p1

CROSSREFS

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686.

KEYWORD

nonn

AUTHOR

Alex Ratushnyak, Jan 24 2018

EXTENSIONS

a(9)-a(25) from Chai Wah Wu, Jan 27 2018

STATUS

approved

A299155

Numbers i such that Fibonacci(i) is divisible by i+k for k=0..6.

+10
2

329400, 175472640, 808214400, 1367566200, 1928871000, 3433706640, 16109533440, 16916445000, 17847413640, 19507068000, 23163310800, 24961167000, 32645743200, 37263088800, 39803400000, 44915270400, 50238568800, 66072283200, 81924990840, 85368457440

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

A subsequence of A298687.

LINKS

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

PROG

(PARI) fibomod(n, m) = lift(Mod([0, 1; 1, 1], m)^(n+1))[1, 1];

isok(n) = prod(k=0, 6, fibomod(n, n+k)==0); \\ Silvester Resnik, May 18 2018

CROSSREFS

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686, A298687.

KEYWORD

nonn

AUTHOR

Chai Wah Wu, Feb 03 2018

EXTENSIONS

a(7)-a(20) from Silvester Resnik, May 18 2018

STATUS

approved

A298688

a(n) is the least i such that Fibonacci(i) is divisible by i+k for all k=0..n.

+10
1

1, 60, 60, 540, 13440, 13440, 329400, 175472640, 50238568800

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

a(0)..a(5) are first terms of sequences A023172, A217738, A298684, A298685, A298686, A298687.

LINKS

Table of n, a(n) for n=0..8.

EXAMPLE

Least i such that Fibonacci(i) is divisible by i and i+1 (cf. A217738) is i=60, therefore a(1)=60.

Least i such that Fibonacci(i) is divisible by i, i+1, ..., i+5 (cf. A298687) is i=13440, therefore a(5)=13440.

CROSSREFS

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686, A298687.

KEYWORD

nonn,hard,more

AUTHOR

Alex Ratushnyak, Jan 24 2018

EXTENSIONS

a(7) from Alois P. Heinz, Jan 25 2018

a(6) inserted by Chai Wah Wu, Jan 26 2018

a(8) from Silvester Resnik, May 18 2018

STATUS

approved

A300555

Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..7.

+10
1

175472640, 44915270400, 50238568800, 439287521400, 572836904640, 589596638400, 735284012400, 778042465200, 987189789600, 1261551677400, 1297640010240, 1307130728400, 1569978804240, 1979830125000, 2705598768600

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

LINKS

Table of n, a(n) for n=1..15.

PROG

(PARI) fibomod(n, m) = lift(Mod([0, 1; 1, 1], m)^(n+1))[1, 1];

isok(n) = prod(k=0, 7, fibomod(n, n+k)==0);

CROSSREFS

Subsequence of A299155.

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686, A298687.

KEYWORD