A385959 -id:A385959 - cp's OEIS frontend

A385958 a(n) is the largest prime p such that b(n) = b(n-1)*(p+1)/(p-1) is an integer (A385959), where b(0) = 1.

3, 5, 7, 5, 13, 3, 29, 31, 17, 37, 3, 5, 7, 5, 229, 47, 241, 23, 89, 271, 137, 277, 3, 557, 19, 311, 313, 5, 7, 5, 13, 3, 4397, 7, 5, 13, 3, 29, 21991, 5, 13, 3, 29, 82471, 677, 733, 227, 27893, 19, 11, 111577, 3, 5, 283, 5, 505663, 15803

Offset: 1

Thomas Ordowski, Jul 13 2025

a(n) = (b(n)+b(n-1))/(b(n)-b(n-1)), where b(n) = A385959(n) is the smallest k such that a(n) is a prime, where b(0) = 1.
a(n) is the largest prime p such that p-1 divides 2*b(n-1).
Note that 3 <= a(n) <= 2*b(n-1)+1.
Does this sequence contain all odd primes?

Martin Fuller, Table of n, a(n) for n = 1..3460

Cf. A065091, A073409, A385959.

allocatemem(2^30);
default(factor_add_primes, 1);
{
my(a,b=1);
for(n=1,100,
  removeprimes(select(p->b%p, addprimes()));
  fordiv(2*b, d, a=2*b/d+1; if(isprime(a),break));
  b+=b*2/(a-1);
  print1(a, ", ");
);
} \\ Martin Fuller, Jul 16 2025

a(n) = A073409(b(n-1)), where b(n) = A385959(n) = Product_{k=1..n} (a(k)+1)/(a(k)-1).

Also tanh(Sum_{k=1..n} arctanh(1/a(k))) = (b(n)-1)/(b(n)+1).

More terms from Morné Louw and Martin Fuller, Jul 15 2025

cp's OEIS Frontend

A385958 a(n) is the largest prime p such that b(n) = b(n-1)*(p+1)/(p-1) is an integer (A385959), where b(0) = 1.

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