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A110635
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Every 7-th term of A083947 such that the self-convolution 7-th power is congruent modulo 49 to A083947, which consists entirely of numbers 1 through 7.
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2
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1, 1, 5, 1, 1, 4, 2, 1, 1, 3, 5, 1, 2, 5, 1, 7, 6, 4, 4, 6, 4, 5, 7, 3, 4, 2, 4, 3, 3, 2, 7, 4, 6, 6, 3, 1, 1, 6, 5, 6, 6, 3, 1, 2, 5, 7, 3, 3, 7, 5, 5, 6, 4, 6, 3, 4, 2, 5, 4, 4, 7, 3, 4, 1, 5, 6, 7, 2, 2, 5, 4, 1, 4, 4, 1, 1, 4, 3, 6, 7, 6, 2, 6, 6, 2, 1, 6, 6, 1, 5, 2, 2, 5, 5, 4, 2, 3, 7, 4, 5, 1, 3, 6, 4, 4
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Congruent modulo 7 to A084207, where the self-convolution 7-th power of A084207 equals A083947.
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FORMULA
| a(n) = A083947(7*n) for n>=0. G.f. satisfies: A(x^7) = G(x) - 7*x*((1-x^6)/(1-x))/(1-x^7), where G(x) is the g.f. of A083947. G.f. satisfies: A(x)^7 = A(x^7) + 7*x*((1-x^6)/(1-x))/(1-x^7) + 49*x^2*H(x) where H(x) is the g.f. of A111584.
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PROG
| (PARI) {a(n)=local(p=7, 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)))}
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CROSSREFS
| Cf. A083947, A111584, A084207.
Sequence in context: A154567 A139391 A196612 * A179773 A071170 A108691
Adjacent sequences: A110632 A110633 A110634 * A110636 A110637 A110638
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com) and Paul D. Hanna (pauldhanna(AT)juno.com), Aug 08 2005
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