A182199 -id:A182199 - cp's OEIS frontend

A182425 a(n) the largest integer K such that (prime(n+1)-1)^(2^k)+1 for 0<=k<=K is prime.

4, 3, 2, 1, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0

Offset: 1

Thomas Ordowski, Apr 28 2012

nonn

This sequence is a generalized reference to Fermat primes.

Cf. A182199.

Table[k = 0; While[PrimeQ[(Prime[n+1] - 1)^(2^k) + 1], k++];  k - 1, {n, 100}] (* T. D. Noe, Apr 28 2012 *)

A283076 Smallest odd prime of the form x^2 + y^2 such that x^(2^k) + y^(2^k) is prime for all k = 1 to n.

Original entry on oeis.org

5, 5, 5, 5, 2823521, 151062433

Offset: 1

Thomas Ordowski and Altug Alkan, Feb 28 2017

			Prime 5 = 2^2 + 1 and 2^4 + 1, 2^8 + 1, 2^16 + 1 are Fermat primes.
Prime 2823521 = 464^2 + 1615^2 is a term.
       a(n)      x      y
  ---------   ----   ----
          5      2      1
          5      2      1
          5      2      1
          5      2      1
    2823521   1615    464
  151062433   9777   7448

Cf. A182199, A282352.

cp's OEIS Frontend

A182425 a(n) the largest integer K such that (prime(n+1)-1)^(2^k)+1 for 0<=k<=K is prime.

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A283076 Smallest odd prime of the form x^2 + y^2 such that x^(2^k) + y^(2^k) is prime for all k = 1 to n.

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