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Search: id:A079394
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| A079394 |
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Compare t(n) and t(n+1) where t = Ramanujan's tau function (A000594); a(n) = pq where p and q are given below. |
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+0
1
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| 21, 31, 21, 31, 21, 11, 31, 21, 11, 31, 22, 11, 32, 41, 42, 21, 32, 41, 22, 12, 11, 31, 41, 21, 32, 21, 32, 41, 22, 11, 11, 32, 41, 22, 31, 21, 11, 12, 31, 42, 42, 22, 11, 12, 12, 31, 42, 21, 32, 21, 32, 21, 31, 41, 22, 31, 21, 11, 12, 31, 42, 41, 41, 21, 11, 11, 32, 42, 42
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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p = 1 if t(n) < 0, t(n+1) < 0; p = 2 if t(n) >= 0, t(n+1) < 0; p = 3 if t(n) < 0, t(n+1) >= 0; p = 4 if t(n) >= 0, t(n+1) >= 0.
q = 1 if |t(n)| <= t(n+1); q = 2 if |t(n)| > t(n+1.
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EXAMPLE
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A000594(1)=1, A000594(2)=-24. Hence the sign changes from + to - and the modulus increasing. Consulting the key, this gives a(1)=21.
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PROGRAM
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(PARI) T(n)=n*(n+1)/2 rtau3(n)=local(y, j); y=0; j=1; while (T(j-1)<n, j++); j--; for (i=1, j, y=y-(-1)^i*(2*i-1)*x^(T(i-1))); y=y^8; polcoeff(y, n-1) for (n=1, 100, r3=rtau3(n); r31=rtau3(n+1); rn=(sign(r3)+1)/2; rn1=sign(r31)+1; print1((rn+rn1+1)""(abs(r3)>abs(r31))+1", "))
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CROSSREFS
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Cf. A000594.
Sequence in context: A115433 A116096 A116116 this_sequence A112375 A067599 A123846
Adjacent sequences: A079391 A079392 A079393 this_sequence A079395 A079396 A079397
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Jan 06 2003
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