A110639 Every 9th term of A083949 where the self-convolution 9th power is congruent modulo 27 to A083949, which consists entirely of numbers 1 through 9.
1, 1, 9, 9, 2, 7, 5, 3, 5, 3, 1, 7, 3, 5, 5, 9, 9, 2, 8, 3, 1, 7, 1, 1, 4, 8, 5, 1, 1, 2, 9, 2, 7, 6, 8, 6, 6, 7, 2, 2, 5, 6, 5, 9, 6, 1, 6, 7, 4, 5, 6, 4, 9, 8, 4, 1, 4, 9, 9, 2, 3, 1, 9, 4, 2, 6, 6, 8, 2, 5, 3, 2, 5, 2, 8, 2, 4, 6, 4, 8, 6, 2, 5, 2, 8, 9, 8, 1, 2, 3, 3, 2, 9, 1, 1, 1, 4, 8, 5, 5, 7, 8, 7, 3, 1
Offset: 0
Keywords
Examples
A(x) = 1 + x + 9*x^2 + 9*x^3 + 2*x^4 + 7*x^5 + 5*x^6 +... A(x)^9 = 1 + 9*x + 117*x^2 + 813*x^3 + 5976*x^4 + 33381*x^5 +... A(x)^9 (mod 27) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 +... G(x) = 1 + 9*x + 9*x^2 + 3*x^3 + 9*x^4 + 9*x^5 + 3*x^6 +... where G(x) is the g.f. of A083949.
Programs
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PARI
{a(n)=local(d=9,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)}