A110642 Every 5th term of A083950 where the self-convolution 5th power is congruent modulo 25 to A083950, which consists entirely of numbers 1 through 10.
1, 2, 3, 2, 5, 8, 8, 4, 7, 2, 7, 4, 7, 2, 9, 6, 8, 8, 8, 8, 5, 8, 6, 2, 10, 4, 1, 4, 5, 6, 5, 10, 4, 4, 6, 10, 8, 4, 2, 8, 3, 10, 6, 10, 2, 8, 2, 6, 6, 4, 2, 10, 4, 8, 4, 10, 3, 2, 6, 2, 4, 2, 3, 8, 10, 10, 3, 6, 10, 10, 6, 8, 5, 8, 6, 4, 10, 2, 2, 4, 8, 2, 10, 4, 9, 6, 1, 6, 5, 10, 9, 8, 2, 8, 10, 4, 7, 8
Offset: 0
Keywords
Examples
A(x) = 1 + 2*x + 3*x^2 + 2*x^3 + 5*x^4 + 8*x^5 + 8*x^6 +... A(x)^5 = 1 + 10*x + 55*x^2 + 210*x^3 + 635*x^4 + 1652*x^5 +... A(x)^5 (mod 25) = 1 + 10*x + 5*x^2 + 10*x^3 + 10*x^4 + 2*x^5 +... G(x) = 1 + 10*x + 5*x^2 + 10*x^3 + 10*x^4 + 2*x^5 + 5*x^6 +... where G(x) is the g.f. of A083950.
Programs
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PARI
{a(n)=local(d=5,m=10,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)}