A298685 -id:A298685 - cp's OEIS frontend

A298686 Numbers i such that Fibonacci(i) is divisible by i+k for k=0,1,2,3,4.

13440, 19440, 19800, 24480, 49680, 61560, 104160, 229320, 298200, 311040, 329400, 436800, 471240, 600600, 1202040, 1299600, 1468800, 1564920, 1702800, 2031120, 2352240, 2402400, 2499840, 2762760, 2805600, 2937600, 2962080, 3150840, 3262680, 3405600, 3843840

Offset: 1

Alex Ratushnyak, Jan 24 2018

nonn

A subsequence of A298685.

Chai Wah Wu, Table of n, a(n) for n = 1..147

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

isone(n, k) = !(fibonacci(n) % (n+k));
isok(n) = isone(n,0) && isone(n,1) && isone(n,2) && isone(n,3) && isone(n,4); \\ Michel Marcus, Jan 28 2018

More terms from Alois P. Heinz, Jan 25 2018

A298687 Numbers i such that Fibonacci(i) is divisible by i+k for k=0..5.

Original entry on oeis.org

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

Offset: 1

Alex Ratushnyak, Jan 24 2018

nonn

A subsequence of A298686.

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

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

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

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

A299155 Numbers i such that Fibonacci(i) is divisible by i+k for k=0..6.

Original entry on oeis.org

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

Offset: 1

Chai Wah Wu, Feb 03 2018

nonn

A subsequence of A298687.

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

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

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

A298688 a(n) is the least i such that Fibonacci(i) is divisible by i+k for all k=0..n.

Original entry on oeis.org

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

Offset: 0

Alex Ratushnyak, Jan 24 2018

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

			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.

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

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

A300555 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..7.

Original entry on oeis.org

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

Offset: 1

Silvester Resnik, May 19 2018

nonn

Subsequence of A299155.

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

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);

A303585 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..8.

Original entry on oeis.org

50238568800, 5824121940000, 46919196354240, 50564131254000, 80493123110400, 195778384956000, 307148642236800, 799863695270640

Offset: 1

Silvester Resnik, May 25 2018

Subsequence of A300555.

Cf. A000045, A023172, A217738, A221018, A225219, A298684, A298685, A298686, A298687, A298688, A299155.

fibomod(n, m) = lift(Mod([0, 1; 1, 1], m)^(n+1))[1, 1];
isok(n) = prod(k=0, 8, fibomod(n, n+k)==0);

cp's OEIS Frontend

A298686 Numbers i such that Fibonacci(i) is divisible by i+k for k=0,1,2,3,4.

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A298687 Numbers i such that Fibonacci(i) is divisible by i+k for k=0..5.

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A299155 Numbers i such that Fibonacci(i) is divisible by i+k for k=0..6.

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A298688 a(n) is the least i such that Fibonacci(i) is divisible by i+k for all k=0..n.

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A300555 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..7.

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A303585 Numbers i such that Fibonacci(i) is divisible by i+k for k = 0..8.

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