A244915 Smallest positive integer a(n) such that b(n) = a(n)^2 + a(n-1)^2 is a prime different from the primes b(1), b(2), ..., b(n-1), where a(0) = 1.

1, 1, 2, 3, 8, 5, 2, 7, 8, 13, 2, 15, 4, 1, 6, 5, 4, 9, 10, 1, 14, 9, 16, 1, 20, 3, 10, 7, 12, 13, 10, 17, 2, 27, 10, 19, 6, 11, 4, 21, 10, 29, 4, 25, 6, 29, 16, 5, 18, 7, 20, 11, 14, 15, 22, 5, 24, 1, 26, 5, 28, 13, 20, 19, 14, 25, 12, 17, 8, 23, 12, 43, 8

Offset: 0

Author

Thomas Ordowski, Aug 21 2014

Keywords

• nonn

Comments

If every positive integer appears in the sequence infinitely often then the sequence b(n) is a permutation of all primes of the form x^2 + y^2.

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A100208.

Programs

PARI

a244915(maxn) = {
  my(a=[1], b=[], an, bn);
  for(n=1, maxn,
    an=1;
    while(!(isprime(bn=an^2+a[#a]^2) && setsearch(b, bn)==0), an++);
    a=concat(a, an);
    b=setunion(b, [bn])
  );
  a
}
a244915(100) \\ Colin Barker, Aug 24 2014

Python

from sympy import isprime
A244915 = [1]
blist = []
for n in range(1, 100):
    a, b = 1, 1 + A244915[-1]**2
    while not isprime(b) or b in blist:
        b += 2*a+1
        a += 1
    blist.append(b)
    A244915.append(a)
# Chai Wah Wu, Aug 28 2014

Extensions

More terms from Colin Barker, Aug 24 2014