A121453 Numbers m such that (m mod k) > (m+2 mod k) with least value of k = 5.

9, 24, 33, 48, 69, 84, 93, 108, 129, 144, 153, 168, 189, 204, 213, 228, 249, 264, 273, 288, 309, 324, 333, 348, 369, 384, 393, 408, 429, 444, 453, 468, 489, 504, 513, 528, 549, 564, 573, 588, 609, 624, 633, 648, 669, 684, 693, 708, 729, 744, 753, 768, 789

Offset

1,1

Comments

Or, numbers m such A121937(m)=5. Cf. A121937 a(n) = least m >= 2 such that (n mod m) > (n+2 mod m).

Links

Table of n, a(n) for n=1..53.

Index entries for linear recurrences with constant coefficients, signature (2, -2, 2, -1).

Formula

a(n) = 3*(sin((n*Pi)/2)- cos((n*Pi)/2)+5*n-3).

a(1)=9, a(2)=24, a(3)=33, a(4)=48, a(n)=2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4). Empirical G.f.: 3*x*(3+2*x+x^2+4*x^3)/(1-2*x+2*x^2-2*x^3+x^4). [Colin Barker, Jan 25 2012]

Example

9 is here because least k such that (9 mod k) > (11 mod k) is 5;
24 is here because least k such that (24 mod k) > (26 mod k) is 5.

Mathematica

Table[15*n-9-3*Cos[(n*Pi)/2]+3*Sin[(n*Pi)/2], {n, 60}]
LinearRecurrence[{2, -2, 2, -1}, {9, 24, 33, 48}, 60] (* Harvey P. Dale, Mar 28 2013 *)

Crossrefs

Cf. A121937.

Sequence in context: A317493 A102217 A124065 * A003343 A345843 A047720

Adjacent sequences: A121450 A121451 A121452 * A121454 A121455 A121456

Keyword

nonn

Author

Zak Seidov, Sep 07 2006

Status

approved