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Search: id:A064526
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| A064526 |
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Define a pair of sequences by p(0)=0, q(0)=p(1)=q(1)=1, q(n+1)=p(n)*q(n-1), p(n+1)=q(n+1)+q(n) for n>0; sequence give p(n); A064183 gives q(n). |
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+0
9
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| 0, 1, 2, 3, 5, 13, 49, 529, 21121, 10369921, 213952189441, 2214253468601687041, 473721461635593679669210030081, 1048939288228833101089604217183056027094304481281
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Every nonzero term is relatively prime to all others.
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REFERENCES
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M. Somos and R. Haas, A linked pair of sequences implies the primes are infinite, Amer. Math. Monthly, 110 (No. 6, 2003), 539-540.
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FORMULA
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a(n)=(a(n-1)^2+a(n-2)^2-a(n-1)*a(n-2)*(1+a(n-2)))/(1-a(n-2)).
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PROGRAM
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(PARI) a(n)=local(v); if(n<3, max(0, n), v=[1, 1]; for(k=3, n, v=[v[2], v[1]*(v[1]+v[2])]); v[1]+v[2])
(PARI) a(n)=if(n<4, max(0, n), (a(n-1)^2+a(n-2)^2-a(n-1)*a(n-2)*(1+a(n-2)))/(1-a(n-2)))
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CROSSREFS
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Cf. A001685, A003686.
Sequence in context: A012899 A110364 A111288 this_sequence A103594 A042695 A074394
Adjacent sequences: A064523 A064524 A064525 this_sequence A064527 A064528 A064529
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KEYWORD
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nonn,easy
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AUTHOR
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Michael Somos, Oct 07, 2001
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