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.
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, 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, 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
Offset: 0
Keywords
Examples
A(x) = 1 + 3*x + 3*x^2 + x^3 + 6*x^4 + 6*x^5 + 9*x^6 +... A(x)^3 = 1 + 9*x + 36*x^2 + 84*x^3 + 144*x^4 + 252*x^5 +... A(x)^3 (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=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)}