cp's OEIS Frontend

A110635 Every 7th term of A083947 such that the self-convolution 7th power is congruent modulo 49 to A083947, which consists entirely of numbers 1 through 7.

%I A110635 #6 Mar 12 2015 22:23:38
%S A110635 1,1,5,1,1,4,2,1,1,3,5,1,2,5,1,7,6,4,4,6,4,5,7,3,4,2,4,3,3,2,7,4,6,6,
%T A110635 3,1,1,6,5,6,6,3,1,2,5,7,3,3,7,5,5,6,4,6,3,4,2,5,4,4,7,3,4,1,5,6,7,2,
%U A110635 2,5,4,1,4,4,1,1,4,3,6,7,6,2,6,6,2,1,6,6,1,5,2,2,5,5,4,2,3,7,4,5,1,3,6,4,4
%N A110635 Every 7th term of A083947 such that the self-convolution 7th power is congruent modulo 49 to A083947, which consists entirely of numbers 1 through 7.
%C A110635 Congruent modulo 7 to A084207, where the self-convolution 7th power of A084207 equals A083947.
%F A110635 a(n) = A083947(7*n) for n>=0.
%F A110635 G.f. satisfies: A(x^7) = G(x) - 7*x*((1-x^6)/(1-x))/(1-x^7), where G(x) is the g.f. of A083947.
%F A110635 G.f. satisfies: A(x)^7 = A(x^7) + 7*x*((1-x^6)/(1-x))/(1-x^7) + 49*x^2*H(x) where H(x) is the g.f. of A111584.
%o A110635 (PARI) {a(n)=local(p=7,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 A110635 Cf. A083947, A111584, A084207.
%K A110635 nonn
%O A110635 0,3
%A A110635 _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 08 2005