

A231831


a(0) = 1; for n > 0, a(n) = 1 + 4*Product_{i=0..n1} a(i)^2.


5




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



FORMULA

For n > 1, a(n) = (a(n1) + 1) * a(n1)^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, n1, a[i]^2)  1; ); a; }


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



