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A032769 Numbers that are congruent to {0, 1, 2, 4} mod 5. 3
0, 1, 2, 4, 5, 6, 7, 9, 10, 11, 12, 14, 15, 16, 17, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 31, 32, 34, 35, 36, 37, 39, 40, 41, 42, 44, 45, 46, 47, 49, 50, 51, 52, 54, 55, 56, 57, 59, 60, 61, 62, 64, 65, 66, 67, 69, 70, 71, 72, 74, 75, 76, 77, 79, 80, 81, 82, 84, 85 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Also, numbers m such that m*(m+1)*(m+2)*(m+3)*(m+4)/(m+(m+1)+(m+2)+(m+3)+(m+4)) is an integer.
LINKS
FORMULA
a(n) = (1/8)*(10*n-1-(-1)^n-2*(-1)^(n/2-1/2). - Ralf Stephan, Jun 09 2005
a(n) = floor((5*n-4)/4). - Gary Detlefs, Mar 06 2010
G.f.: x^2*(1+x+2*x^2+x^3) / ( (1+x)*(1+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
From Wesley Ivan Hurt, May 30 2016: (Start)
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
a(n) = (10*n-11+i^(2*n)+(1+i)*I^(-n)+(1-i)*i^n)/8 where i=sqrt(-1).
a(2k) = A047209(k), a(2k-1) = A047215(k). (End)
E.g.f.: (4 + sin(x) + cos(x) + (5*x - 6)*sinh(x) + 5*(x - 1)*cosh(x))/4. - Ilya Gutkovskiy, May 31 2016
Sum_{n>=2} (-1)^n/a(n) = log(5)/4 + 3*sqrt(5)*log(phi)/10 - sqrt(1-2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 10 2021
MAPLE
seq(floor((5*n-4)/4), n=1..69); # Gary Detlefs, Mar 06 2010
MATHEMATICA
Table[Floor[(5n - 4)/4], {n, 80}] (* Wesley Ivan Hurt, May 30 2016 *)
PROG
(Magma) [Floor((5*n - 4)/4) : n in [1..80]]; // Wesley Ivan Hurt, May 30 2016
CROSSREFS
Sequence in context: A039186 A184516 A184738 * A039139 A349829 A230633
KEYWORD
nonn,easy
AUTHOR
Patrick De Geest, May 15 1998
EXTENSIONS
Better description from Michael Somos, Jun 08 2000
STATUS
approved

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Last modified March 29 05:48 EDT 2024. Contains 371265 sequences. (Running on oeis4.)