A110631 Every 5th term of A083945 such that the self-convolution 5th power is congruent modulo 25 to A083945, which consists entirely of numbers 1 through 5.

1, 1, 4, 3, 2, 4, 4, 2, 1, 5, 2, 1, 5, 1, 3, 2, 5, 3, 4, 4, 5, 4, 5, 2, 1, 5, 4, 1, 2, 5, 1, 5, 1, 1, 1, 2, 3, 4, 2, 2, 4, 3, 2, 5, 2, 3, 5, 1, 1, 2, 3, 3, 1, 1, 2, 2, 3, 4, 4, 1, 2, 1, 3, 4, 1, 4, 2, 3, 5, 4, 4, 3, 5, 3, 4, 2, 2, 4, 2, 2, 5, 3, 2, 4, 2, 5, 5, 5, 3, 5, 4, 4, 1, 3, 5, 1, 5, 5, 4, 3, 5, 2, 2, 2, 5

Offset

0,3

Comments

Congruent modulo 5 to A084205, where the self-convolution 5th power of A084205 equals A083945.

Links

Table of n, a(n) for n=0..104.

Formula

a(n) = A083945(5*n) for n>=0.

G.f. satisfies: A(x^5) = G(x) - 5*x*((1-x^4)/(1-x))/(1-x^5), where G(x) is the g.f. of A083945.

G.f. satisfies: A(x)^5 = A(x^5) + 5*x*((1-x^4)/(1-x))/(1-x^5) + 25*x^2*H(x) where H(x) is the g.f. of A111583.

Prog

(PARI) {a(n)=local(p=5, A, C, X=x+x*O(x^(p*n))); if(n==0, 1, A=sum(i=0, n-1, a(i)*x^(p*i))+p*x*((1-x^(p-1))/(1-X))/(1-X^p); for(k=1, p, C=polcoeff((A+k*x^(p*n))^(1/p), p*n); if(denominator(C)==1, return(k); break)))}

Crossrefs

Cf. A083945, A111583, A084205.

Sequence in context: A184412 A304240 A244951 * A333669 A159846 A377512

Adjacent sequences: A110628 A110629 A110630 * A110632 A110633 A110634

Keyword

nonn

Author

Robert G. Wilson v and Paul D. Hanna, Aug 08 2005

Status

approved