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A047204
Numbers that are congruent to {3, 4} mod 5.
23
3, 4, 8, 9, 13, 14, 18, 19, 23, 24, 28, 29, 33, 34, 38, 39, 43, 44, 48, 49, 53, 54, 58, 59, 63, 64, 68, 69, 73, 74, 78, 79, 83, 84, 88, 89, 93, 94, 98, 99, 103, 104, 108, 109, 113, 114, 118, 119, 123, 124, 128, 129, 133, 134, 138, 139, 143, 144, 148, 149
OFFSET
1,1
COMMENTS
Also numbers that cannot be expressed as the sum of two 4th powers. - Cino Hilliard, Nov 23 2003
The sequence lists the indices of the multiples of 5 in A033567. - Bruno Berselli, Jan 05 2018
FORMULA
a(n) = 5*n - a(n-1) - 3 for n>1, a(1)=3. - Vincenzo Librandi, Nov 18 2010
G.f.: x*(3 + x + x^2) / ((1 + x)*(x - 1)^2). - R. J. Mathar, Oct 08 2011
a(n) = floor(5*n/2) - (-1)^n. - Wesley Ivan Hurt, Sep 12 2017
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2-2/sqrt(5))*Pi/10 - sqrt(5)*log(phi)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Dec 07 2021
E.g.f.: 1 + ((10*x - 1)*exp(x) - 3*exp(-x))/4. - David Lovler, Aug 23 2022
MATHEMATICA
Select[Range[0, 200], MemberQ[{3, 4}, Mod[#, 5]] &] (* Vladimir Joseph Stephan Orlovsky, Feb 12 2012 *)
PROG
(PARI) a(n)=(n-1)\2*5+4-n%2 \\ Charles R Greathouse IV, Dec 22 2011
CROSSREFS
Sequence in context: A310017 A191285 A219658 * A050035 A306901 A355477
KEYWORD
nonn,easy
STATUS
approved