A110636 Every 8th term of A083948 where the self-convolution 8th power is congruent modulo 16 to A083948, which consists entirely of numbers 1 through 8.
1, 7, 3, 1, 6, 6, 4, 8, 7, 8, 8, 7, 3, 3, 3, 1, 4, 3, 6, 5, 1, 6, 6, 1, 1, 5, 4, 8, 5, 5, 4, 6, 5, 8, 7, 6, 5, 6, 6, 5, 8, 4, 7, 4, 1, 3, 7, 7, 4, 6, 8, 7, 4, 8, 8, 1, 5, 3, 5, 5, 6, 2, 4, 4, 7, 2, 6, 2, 1, 4, 3, 5, 5, 3, 5, 1, 5, 3, 7, 8, 6, 5, 1, 2, 1, 1, 2, 4, 6, 1, 6, 3, 5, 1, 7, 3, 4, 2, 6, 7, 1, 3, 1, 8, 3
Offset: 0
Keywords
Examples
A(x) = 1 + 7*x + 3*x^2 + x^3 + 6*x^4 + 6*x^5 + 4*x^6 + 8*x^7 +... A(x)^8 = 1 + 56*x + 1396*x^2 + 20392*x^3 + 193458*x^4 +... A(x)^8 (mod 16) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 +... G(x) = 1 + 8*x + 4*x^2 + 8*x^3 + 2*x^4 + 8*x^5 + 4*x^6 +... where G(x) is the g.f. of A083948.
Programs
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PARI
{a(n)=local(d=8,m=8,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)}