A108972 - OEIS

A108972

a(1) = 1; for n > 1, a(n) is the least k > a(n-1) such that a(n) + a(n-1) is square and a(n) - a(n-1) is prime.

%I #4 Oct 02 2013 15:12:46

%S 1,3,6,19,30,91,134,307,318,1051,1158,1867,2358,2971,3590,3979,4670,

%T 5131,5478,7747,7878,8251,8390,16891,17334,22267,28358,30691,31310,

%U 36811,37718,61507,64518,70171,70454,74707,76614,79411,79790,89131

%N a(1) = 1; for n > 1, a(n) is the least k > a(n-1) such that a(n) + a(n-1) is square and a(n) - a(n-1) is prime.

%e Given a(5) = 30, the least k > 30 such that k + 30 is square and k - 30 is prime is 91 (91 + 30 = 121 = 11^2; and 91 - 30 = 61 is prime), so a(6) = 91.

%t a = 1; Print[a]; Do[k = a + 1; While[ !(PrimeQ[k - a] && IntegerQ[Sqrt[k + a]]), k++ ]; a = k; Print[a], {n, 1, 30}]

%Y Cf. A090956.

%K nonn

%O 1,2

%A _Ryan Propper_, Aug 27 2005

%E More terms from _Robert G. Wilson v_, Sep 28 2005