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A062067 a(1) = 1; a(n) is smallest square > a(n-1) such that a(n) + a(n-1) is a prime.

%I A062067 #26 Aug 05 2021 16:14:02
%S A062067 1,4,9,64,169,400,529,900,961,1936,2401,5476,6241,6400,7921,9216,
%T A062067 10201,10816,11025,13456,14161,15376,17161,17956,19321,19600,22201,
%U A062067 22500,24649,24964,27225,29584,29929,31684,33489,40804,41209,52900
%N A062067 a(1) = 1; a(n) is smallest square > a(n-1) such that a(n) + a(n-1) is a prime.
%H A062067 Harry J. Smith, <a href="/A062067/b062067.txt">Table of n, a(n) for n = 1..1000</a>
%e A062067 9 is the next term after 4 as 4+9 = 13 is a prime.
%t A062067 sqrs=Range[400]^2;
%t A062067 nxt[n_]:=First[Select[sqrs,#>n&&PrimeQ[n+#]&]]
%t A062067 NestList[nxt,1,45]  (* _Harvey P. Dale_, Dec 26 2010 *)
%o A062067 (PARI) p=1;n=2;for(k=1,50, while(!isprime(p^2+n^2),n=n+1);print1(n^2",");p=n;n=n+1)
%o A062067 (PARI) { a=b=1; for (n=1, 1000, if (n>1, until (isprime(a + b^2), b++)); write("b062067.txt", n, " ", a=b^2) ) } \\ _Harry J. Smith_, Jul 31 2009
%o A062067 (Python)
%o A062067 from sympy import isprime
%o A062067 A062067, a = [1], 1
%o A062067 for _ in range(1,10000):
%o A062067     a += 1
%o A062067     b = 2*a*(a-1) + 1
%o A062067     while not isprime(b):
%o A062067         b += 4*(a+1)
%o A062067         a += 2
%o A062067     A062067.append(a**2) # _Chai Wah Wu_, Sep 01 2014
%K A062067 nonn
%O A062067 1,2
%A A062067 _Amarnath Murthy_, Jun 12 2001
%E A062067 Corrected and extended by _Ralf Stephan_, Mar 22 2003