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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Congruent modulo 5 to A084205, where the self-convolution 5th power of A084205 equals A083945. LINKS 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 A071890 Adjacent sequences:  A110628 A110629 A110630 * A110632 A110633 A110634 KEYWORD nonn AUTHOR Robert G. Wilson v and Paul D. Hanna, Aug 08 2005 STATUS approved

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Last modified May 6 19:52 EDT 2021. Contains 343586 sequences. (Running on oeis4.)