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Search: id:A110631
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| A110631 |
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Every 5-th term of A083945 such that the self-convolution 5-th power is congruent modulo 25 to A083945, which consists entirely of numbers 1 through 5. |
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3
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| 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; listen)
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OFFSET
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0,3
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COMMENT
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Congruent modulo 5 to A084205, where the self-convolution 5-th power of A084205 equals A083945.
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FORMULA
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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.
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PROGRAM
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(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)))}
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CROSSREFS
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Cf. A083945, A111583, A084205.
Sequence in context: A152062 A084255 A076576 this_sequence A159846 A071890 A021702
Adjacent sequences: A110628 A110629 A110630 this_sequence A110632 A110633 A110634
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KEYWORD
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nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com) and Paul D. Hanna (pauldhanna(AT)juno.com), Aug 08 2005
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