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%I #6 Mar 13 2015 19:19:40
%S 1,1,4,3,2,4,4,2,1,5,2,1,5,1,3,2,5,3,4,4,5,4,5,2,1,5,4,1,2,5,1,5,1,1,
%T 1,2,3,4,2,2,4,3,2,5,2,3,5,1,1,2,3,3,1,1,2,2,3,4,4,1,2,1,3,4,1,4,2,3,
%U 5,4,4,3,5,3,4,2,2,4,2,2,5,3,2,4,2,5,5,5,3,5,4,4,1,3,5,1,5,5,4,3,5,2,2,2,5
%N Every 5th term of A083945 such that the self-convolution 5th power is congruent modulo 25 to A083945, which consists entirely of numbers 1 through 5.
%C Congruent modulo 5 to A084205, where the self-convolution 5th power of A084205 equals A083945.
%F a(n) = A083945(5*n) for n>=0.
%F G.f. satisfies: A(x^5) = G(x) - 5*x*((1-x^4)/(1-x))/(1-x^5), where G(x) is the g.f. of A083945.
%F G.f. satisfies: A(x)^5 = A(x^5) + 5*x*((1-x^4)/(1-x))/(1-x^5) + 25*x^2*H(x) where H(x) is the g.f. of A111583.
%o (PARI) {a(n)=local(p=5,A,C,X=x+x*O(x^(p*n)));if(n==0,1, A=sum(i=0,n-1,a(i)*x^(p*i))+p*x*((1-x^(p-1))/(1-X))/(1-X^p); for(k=1,p,C=polcoeff((A+k*x^(p*n))^(1/p),p*n); if(denominator(C)==1,return(k);break)))}
%Y Cf. A083945, A111583, A084205.
%K nonn
%O 0,3
%A _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 08 2005
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