cp's OEIS Frontend

A110640 Every third term of A083949 where the self-convolution third power is congruent modulo 27 to A083949, which consists entirely of numbers 1 through 9.

%I A110640 #6 Mar 30 2012 18:36:50
%S A110640 1,3,3,1,6,6,9,6,6,9,3,3,2,6,6,7,9,9,5,9,9,3,6,6,5,9,9,3,9,9,1,6,6,7,
%T A110640 6,6,3,9,9,5,3,3,5,9,9,9,9,9,9,6,6,2,9,9,8,3,3,3,3,3,1,3,3,7,9,9,1,6,
%U A110640 6,1,9,9,4,3,3,8,9,9,5,3,3,1,6,6,1,6,6,2,9,9,9,9,9,2,6,6,7,3,3,6,6,6,8,9,9
%N A110640 Every third term of A083949 where the self-convolution third power is congruent modulo 27 to A083949, which consists entirely of numbers 1 through 9.
%e A110640 A(x) = 1 + 3*x + 3*x^2 + x^3 + 6*x^4 + 6*x^5 + 9*x^6 +...
%e A110640 A(x)^3 = 1 + 9*x + 36*x^2 + 84*x^3 + 144*x^4 + 252*x^5 +...
%e A110640 A(x)^3 (mod 27) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 +...
%e A110640 G(x) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6 +...
%e A110640 where G(x) is the g.f. of A083949.
%o A110640 (PARI) {a(n)=local(d=3,m=9,A=1+m*x); for(j=2,d*n, for(k=1,m,t=polcoeff((A+k*x^j+x*O(x^j))^(1/m),j); if(denominator(t)==1,A=A+k*x^j;break)));polcoeff(A,d*n)}
%Y A110640 Cf. A083949, A110639.
%K A110640 nonn
%O A110640 0,2
%A A110640 _Robert G. Wilson v_ and _Paul D. Hanna_, Aug 30 2005