A231830 - OEIS

A231830

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

1, 5, 101, 1020101, 1061522231810040101, 1196154511175776540960913502483611007728163340227060101

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OFFSET

0,2

COMMENTS

Sequence designed to show that there are an infinity of primes congruent to 1 modulo 4 (A002144). Terms are not necessarily prime. Their smallest prime factors from A002144 are: 5, 101, 1020101, 53, 686743037.

Next term is too large to include.

From Max Alekseyev, Apr 21 2023: (Start)

Similarly to Sylvester's sequence (A000058), it is unknown if all terms are squarefree.

Primes dividing terms of this sequence are listed in A362252. Since terms are pairwise coprime, for each n prime A362252(n) divides exactly one term, whose index is A362253(n). That is, A362252(n) divides a(A362253(n)). (End)

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.

FORMULA

For n > 1, a(n) = (a(n-1) - 1) * a(n-1)^2 + 1. - Max Alekseyev, Mar 25 2023

PROG

(PARI) lista(nn) = {a = vector(nn); a[1] = 5; for (n=2, nn, a[n] = 4*prod(i=1, n-1, a[i]^2) + 1; ); a; }

CROSSREFS

Cf. A000058, A002144, A007018, A231831, A362252, A362253.

Sequence in context: A275749 A057207 A124986 * A260024 A123626 A210900

Adjacent sequences: A231827 A231828 A231829 * A231831 A231832 A231833

KEYWORD

nonn

AUTHOR

Michel Marcus, Nov 14 2013

EXTENSIONS

a(0)=1 prepended by Max Alekseyev, Mar 25 2023

STATUS

approved