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 A231831 a(0) = 1; for n > 0, a(n) = -1 + 4*Product_{i=0..n-1} a(i)^2. 5
 1, 3, 35, 44099, 85762231424099, 630794963141019085083178800095033630804099 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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 LINKS Table of n, a(n) for n=0..5. S. A. Shirali, A family portrait of primes-a case study in discrimination, Math. Mag. Vol. 70, No. 4 (Oct., 1997), pp. 263-272. fredrickmnelson et al., Does a(0)=6, a(n+1)=a(n)^3-a(n), define a square-free sequence?, MathOverflow, 2023. FORMULA For n > 1, a(n) = (a(n-1) + 1) * a(n-1)^2 - 1. - Max Alekseyev, Mar 26 2023 PROG (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; } CROSSREFS Cf. A000058, A002145, A007018, A231830, A362250, A362251. Sequence in context: A134098 A132513 A034174 * A119526 A112404 A189216 Adjacent sequences: A231828 A231829 A231830 * A231832 A231833 A231834 KEYWORD nonn AUTHOR Michel Marcus, Nov 14 2013 EXTENSIONS a(0) = 1 prepended by Max Alekseyev, Mar 26 2023 STATUS approved

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Last modified September 21 19:25 EDT 2023. Contains 365503 sequences. (Running on oeis4.)