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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.

%I A244915 #104 Sep 24 2024 02:13:34
%S A244915 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 A244915 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 A244915 5,24,1,26,5,28,13,20,19,14,25,12,17,8,23,12,43,8
%N 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.
%C A244915 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 A244915 Jens Kruse Andersen, <a href="/A244915/b244915.txt">Table of n, a(n) for n = 0..10000</a>
%o A244915 (PARI)
%o A244915 a244915(maxn) = {
%o A244915   my(a=[1], b=[], an, bn);
%o A244915   for(n=1, maxn,
%o A244915     an=1;
%o A244915     while(!(isprime(bn=an^2+a[#a]^2) && setsearch(b, bn)==0), an++);
%o A244915     a=concat(a, an);
%o A244915     b=setunion(b, [bn])
%o A244915   );
%o A244915   a
%o A244915 }
%o A244915 a244915(100) \\ _Colin Barker_, Aug 24 2014
%o A244915 (Python)
%o A244915 from sympy import isprime
%o A244915 A244915 = [1]
%o A244915 blist = []
%o A244915 for n in range(1, 100):
%o A244915     a, b = 1, 1 + A244915[-1]**2
%o A244915     while not isprime(b) or b in blist:
%o A244915         b += 2*a+1
%o A244915         a += 1
%o A244915     blist.append(b)
%o A244915     A244915.append(a)
%o A244915 # _Chai Wah Wu_, Aug 28 2014
%Y A244915 Cf. A100208.
%K A244915 nonn
%O A244915 0,3
%A A244915 _Thomas Ordowski_, Aug 21 2014
%E A244915 More terms from _Colin Barker_, Aug 24 2014