A110638 Every 2nd term of A083948 where the self-convolution 2nd power is congruent modulo 16 to A083948, which consists entirely of numbers 1 through 8.
1, 4, 2, 4, 7, 8, 4, 8, 3, 8, 2, 8, 1, 8, 8, 8, 6, 4, 6, 4, 6, 8, 4, 8, 4, 8, 2, 8, 8, 8, 8, 8, 7, 8, 6, 8, 8, 4, 6, 4, 8, 8, 6, 8, 7, 4, 8, 4, 3, 4, 4, 4, 3, 8, 6, 8, 3, 8, 8, 8, 1, 8, 4, 8, 4, 8, 8, 8, 3, 8, 6, 8, 6, 8, 2, 8, 5, 8, 8, 8, 1, 8, 4, 8, 6, 4, 4, 4, 6, 8, 6, 8, 1, 4, 8, 4, 1, 8, 6, 8, 5, 4, 8, 4, 4
Offset: 0
Keywords
Examples
A(x) = 1 + 4*x + 2*x^2 + 4*x^3 + 7*x^4 + 8*x^5 + 4*x^6 +... A(x)^2 = 1 + 8*x + 20*x^2 + 24*x^3 + 50*x^4 + 88*x^5 +... A(x)^2 (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=2,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)}