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A231831
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a(0) = 1; for n > 0, a(n) = -1 + 4*Product_{i=0..n-1} a(i)^2.
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5
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OFFSET
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0,2
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COMMENTS
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Sequence designed to show that there are an infinity of primes congruent to 3 modulo 4 (A002145). Terms are not necessarily prime. Their smallest prime factor from A002145 are: 3, 7, 11, 23, 4111, 2809343.
Next term is too large to include.
Similarly to Sylvester's sequence (A000058), it is unknown if all terms are squarefree (see also MathOverflow link). - Max Alekseyev, Mar 26 2023
Primes dividing terms of this sequence are listed in A362250. Since terms are pairwise coprime, for each n prime A362250(n) divides exactly one term, whose index is A362251(n). That is, A362250(n) divides a(A362251(n)). - Max Alekseyev, Apr 16 2023
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LINKS
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FORMULA
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For n > 1, a(n) = (a(n-1) + 1) * a(n-1)^2 - 1. - Max Alekseyev, Mar 26 2023
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PROG
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(PARI) lista(nn) = {a = vector(nn); a[1] = 3; for (n=2, nn, a[n] = 4*prod(i=1, n-1, a[i]^2) - 1; ); a; }
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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