A295388 a(n) is the least k > n such that n divides k, and n+1 divides k+1, and n+2 divides k+2.

7, 14, 63, 64, 215, 174, 511, 368, 999, 670, 1727, 1104, 2743, 1694, 4095, 2464, 5831, 3438, 7999, 4640, 10647, 6094, 13823, 7824, 17575, 9854, 21951, 12208, 26999, 14910, 32767, 17984, 39303, 21454, 46655, 25344, 54871, 29678, 63999, 34480, 74087, 39774, 85183

Offset

1,1

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -6, 0, 4, 0, -1).

Formula

a(2n-1) = 8*n^3 - 1.

a(2n) = 4*n^3 + 6*n^2 + 4*n.

G.f.: (7 + 14*x + 35*x^2 + 8*x^3 + 5*x^4 + 2*x^5 + x^6)/(x^2 - 1)^4.

Example

999 is the smallest integer k > 9 such that 9 divides k, 10 divides k+1, and 11 divides k+2. Therefore a(9)=999.

Mathematica

f[n_] := Block[{k = 2 n}, While[ Mod[{k, k +1, k +2}, {n, n +1, n +2}] != {0, 0, 0}, k += n]; k]; Array[f, 45] (* or *)
CoefficientList[ Series[(7 + 14x + 35x^2 + 8x^3 + 5 x^4 + 2x^5 + x^6)/(x^2 - 1)^4, {x, 0, 50}], x] (* or *)
LinearRecurrence[{0, 4, 0, -6, 0, 4, 0, -1}, {7, 14, 63, 64, 215, 174,
   511, 368}, 50] (* Robert G. Wilson v, Feb 12 2018 *)

Prog

(PARI) a(n) = {my(k=n+1); while ((k % n) || ((k+1) % (n+1)) || ((k+2) % (n+2)), k++); k; } \\ Michel Marcus, Feb 12 2018

Crossrefs

Cf. A005563 (with only: n divides k, and n+1 divides k+1).

Sequence in context: A033650 A135536 A241201 * A020700 A110496 A117867

Adjacent sequences: A295385 A295386 A295387 * A295389 A295390 A295391

Keyword

nonn,easy

Author

Alex Ratushnyak, Feb 03 2018

Status

approved