A047540 Numbers that are congruent to {0, 2, 4, 7} mod 8.

0, 2, 4, 7, 8, 10, 12, 15, 16, 18, 20, 23, 24, 26, 28, 31, 32, 34, 36, 39, 40, 42, 44, 47, 48, 50, 52, 55, 56, 58, 60, 63, 64, 66, 68, 71, 72, 74, 76, 79, 80, 82, 84, 87, 88, 90, 92, 95, 96, 98, 100, 103, 104, 106, 108, 111, 112, 114, 116, 119, 120, 122, 124

Offset

1,2

Comments

The products of an odd number of terms as well as products of one term each of this sequence and one term of A047409 are members. The products of an even number of terms belong to A047409. The union of this sequence and A047409 is closed under multiplication. - Klaus Purath, Apr 23 2023

Links

Table of n, a(n) for n=1..63.

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

Formula

From Wesley Ivan Hurt, May 29 2016: (Start)

G.f.: x^2*(2+2*x+3*x^2+x^3) / ((x-1)^2*(1+x+x^2+x^3)).

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

a(n) = (8*n-7+i^(2*n)+i^(-n)+i^n)/4 where i=sqrt(-1).

a(2k) = A047524(k), a(2k-1) = A008586(k-1) for k>0. (End)

Sum_{n>=2} (-1)^n/a(n) = (10-sqrt(2))*log(2)/16 + sqrt(2)*log(2+sqrt(2))/8 - sqrt(2)*Pi/16. - Amiram Eldar, Dec 21 2021

Maple

A047540:=n->(8*n-7+I^(2*n)+I^(-n)+I^n)/4: seq(A047540(n), n=1..100); # Wesley Ivan Hurt, May 29 2016

Mathematica

Table[(8n-7+I^(2n)+I^(-n)+I^n)/4, {n, 80}] (* Wesley Ivan Hurt, May 29 2016 *)
{0, 2, 4, 7}+#&/@(8*Range[0, 20])//Flatten (* Harvey P. Dale, Dec 20 2022 *)

Prog

(Magma) [n : n in [0..150] | n mod 8 in [0, 2, 4, 7]]; // Wesley Ivan Hurt, May 29 2016

Crossrefs

Cf. A008586, A047524.

Sequence in context: A248637 A131346 A341350 * A116478 A207829 A207827

Adjacent sequences: A047537 A047538 A047539 * A047541 A047542 A047543

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved