A244915 - OEIS

%I #104 Sep 24 2024 02:13:34

%S 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,

%T 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,

%U 5,24,1,26,5,28,13,20,19,14,25,12,17,8,23,12,43,8

%N 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.

%C 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.

%H Jens Kruse Andersen, <a href="/A244915/b244915.txt">Table of n, a(n) for n = 0..10000</a>

%o (PARI)

%o a244915(maxn) = {

%o   my(a=[1], b=[], an, bn);

%o   for(n=1, maxn,

%o     an=1;

%o     while(!(isprime(bn=an^2+a[#a]^2) && setsearch(b, bn)==0), an++);

%o     a=concat(a, an);

%o     b=setunion(b, [bn])

%o   );

%o   a

%o }

%o a244915(100) \\ _Colin Barker_, Aug 24 2014

%o (Python)

%o from sympy import isprime

%o A244915 = [1]

%o blist = []

%o for n in range(1, 100):

%o     a, b = 1, 1 + A244915[-1]**2

%o     while not isprime(b) or b in blist:

%o         b += 2*a+1

%o         a += 1

%o     blist.append(b)

%o     A244915.append(a)

%o # _Chai Wah Wu_, Aug 28 2014

%Y Cf. A100208.

%K nonn,changed

%O 0,3

%A _Thomas Ordowski_, Aug 21 2014

%E More terms from _Colin Barker_, Aug 24 2014