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A045797 Evenish numbers (prime to 10 and 10's digit is even).

%I A045797 #37 Jan 09 2023 16:53:44
%S A045797 1,3,7,9,21,23,27,29,41,43,47,49,61,63,67,69,81,83,87,89,101,103,107,
%T A045797 109,121,123,127,129,141,143,147,149,161,163,167,169,181,183,187,189,
%U A045797 201,203,207,209,221,223,227,229,241,243,247,249,261,263,267,269,281
%N A045797 Evenish numbers (prime to 10 and 10's digit is even).
%C A045797 From _Jianing Song_, Apr 27 2019: (Start)
%C A045797 Numbers congruent to {1, 3, 7, 9} mod 20.
%C A045797 Numbers k such that Kronecker(-20,k) = A289741(k) = +1. (End)
%C A045797 First 20 terms are congruences of 3^k mod 100. - _Dario Vuksan_, Jan 09 2023
%H A045797 Reinhard Zumkeller, <a href="/A045797/b045797.txt">Table of n, a(n) for n = 1..10000</a>
%H A045797 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A045797 Conjecture a(n) = a(n-1)+a(n-4)-a(n-5). G.f.: x*(1+2*x+4*x^2+2*x^3+11*x^4) / ((1-x)^2*(1+x)*(1+x^2)). - _Colin Barker_, Apr 14 2012
%F A045797 The conjecture above is correct. - _Jianing Song_, Apr 27 2019
%F A045797 a(n) = 5n + O(1). - _Charles R Greathouse IV_, Jan 09 2023
%t A045797 Flatten[Table[10n+{1,3,7,9},{n,0,30,2}]] (* _Harvey P. Dale_, Dec 05 2012 *)
%o A045797 (Haskell)
%o A045797 a045797 n = a045797_list !! (n-1)
%o A045797 a045797_list = filter (even . (`mod` 10) . (`div` 10)) a045572_list
%o A045797 -- _Reinhard Zumkeller_, Dec 10 2011
%o A045797 (PARI) is(n)=gcd(n,10)==1 && n\10%2==0 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A045797 Complement of A045798 with respect to A045572.
%K A045797 nonn,base,easy,nice
%O A045797 1,2
%A A045797 _J. H. Conway_
%E A045797 More terms from _Erich Friedman_
%E A045797 Offset changed by _Reinhard Zumkeller_, Dec 10 2011