A096023 Numbers congruent to {63, 123, 183, 243, 303, 363} mod 420.

63, 123, 183, 243, 303, 363, 483, 543, 603, 663, 723, 783, 903, 963, 1023, 1083, 1143, 1203, 1323, 1383, 1443, 1503, 1563, 1623, 1743, 1803, 1863, 1923, 1983, 2043, 2163, 2223, 2283, 2343, 2403, 2463, 2583, 2643, 2703, 2763, 2823, 2883, 3003, 3063, 3123

Offset: 1

Author

Klaus Brockhaus, Jun 15 2004

Keywords

• nonn
• easy

Comments

Numbers n such that (n+j) mod (2+j) = 1 for j from 0 to 4 and (n+5) mod 7 <> 1.

Numbers n such that n mod 60 = 3 and n mod 420 <> 3.

Examples

			63 mod 2 = 64 mod 3 = 65 mod 4 = 66 mod 5 = 67 mod 6 = 1 and 68 mod 7 = 5, hence 63 is in the sequence.
		

Links

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

Crossrefs

Cf. A007310, A017629, A096022, A096024, A096025, A096026, A096027.

Cf. A047391 (see MAGMA code). - Bruno Berselli, Mar 25 2011

Programs

Magma

[ n : n in [1..3500] | n mod 420 in [63, 123, 183, 243, 303, 363] ] // Vincenzo Librandi, Mar 24 2011

Magma

/* Alternatively:*/ &cat[ [ 60*n+3, 60*n+63 ]: n in [1..52] | n mod 7 in [1,3,5] ]; // Bruno Berselli, Mar 25 2011

Maple

A096023:=n->420*floor(n/6)+[63, 123, 183, 243, 303, 363][(n mod 6)+1]: seq(A096023(n), n=0..80); # Wesley Ivan Hurt, Jul 22 2016

Mathematica

Select[Range[0, 5*10^3], MemberQ[{63, 123, 183, 243, 303, 363}, Mod[#, 420]] &] (* Wesley Ivan Hurt, Jul 22 2016 *)

PARI

{k=5;m=3150;for(n=1,m,j=0;b=1;while(b&&j
				

Formula

G.f.: 3*x*(21+20*x+20*x^2+20*x^3+20*x^4+20*x^5+19*x^6) / ( (1+x)*(1+x+x^2)*(x^2-x+1)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011

From Wesley Ivan Hurt, Jul 22 2016: (Start)

a(n) = a(n-1) + a(n-6) - a(n-7) for n>7; a(n) = a(n-6) + 420 for n>6.

a(n) = (210*n - 96 - 30*cos(n*Pi/3) - 30*cos(2*n*Pi/3) - 15*cos(n*Pi) + 30*sqrt(3)*sin(n*Pi/3) + 10*sqrt(3)*sin(2*n*Pi/3))/3.

a(6k) = 420k-57, a(6k-1) = 420k-117, a(6k-2) = 420k-177, a(6k-3) = 420k-237, a(6k-4) = 420k-297, a(6k-5) = 420k-357. (End)

Extensions

New definition from Ralf Stephan, Dec 01 2004