A219634 a(n) is the smallest number > a(n-1) such that 1 + a(1)^2 + a(2)^2 + ... + a(n)^2 is a prime.

1, 3, 6, 12, 30, 54, 60, 72, 120, 126, 144, 174, 198, 210, 294, 300, 318, 354, 408, 420, 426, 432, 480, 498, 522, 564, 588, 594, 600, 624, 630, 648, 666, 714, 720, 852, 864, 978, 1002, 1050, 1056, 1080, 1098, 1122, 1146, 1152, 1170, 1176, 1200, 1206, 1458

Offset: 1

Author

Michel Lagneau, Nov 24 2012

Keywords

• nonn

Comments

The corresponding primes are 2, 11, 47, 191, 1091, 4007, 7607, 12791, 27191, 43067, ...

Examples

			a(1) = 1 because 1 + 1^2 = 2 is prime;
a(2) = 3 because 1 + 1^2 + 2^2 = 6 is not prime, but 1 + 1^2 + 3^2 = 11 is prime;
a(3) = 6 because neither 1 + 1^2 + 3^2 + 4^2 = 27 nor 1 + 1^2 + 3^2 + 5^2 = 36 is prime, but 1 + 1^2 + 3^2 + 6^2 = 47 is prime.
		

Crossrefs

Cf. A051935.

Programs

Mathematica

p=1;lst={p};Do[If[PrimeQ[p+n^2],AppendTo[lst,n];p=p+n^2],{n,1,1500}];lst