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A047540
Numbers that are congruent to {0, 2, 4, 7} mod 8.
1
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
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
Sequence in context: A248637 A131346 A341350 * A116478 A207829 A207827
KEYWORD
nonn,easy
STATUS
approved