A092120 a(n) is the first term p in a sequence of primes such that p+4m^2 is prime for m = 0 to n, but composite for m = n+1; a(n) = -1 if no such prime exists.

2, 19, 3, 277, 43, 53593, 7, 67, 37, 1483087, 1867783, 9671300983, 376040154163, 13491637509487, 604490757900187, 409333

Offset: 0

Author

Ray G. Opao, Mar 29 2004

Keywords

• nonn

Comments

Similar to A092474 except that a(n)+4m^2 is composite for m = n+1.

a(19)=163. All other terms after a(15) are greater than 10^17 (if they exist). [From Jens Kruse Andersen, Oct 24 2008]

Examples

			a(3) = 277 because 277, 277 + 2^2 = 281, 277 + 4^2 = 293, and 277 + 6^2 = 313 are all prime, but 277 + 8^2 = 341 = 11*31 is composite, and there is no smaller prime with this property.
a(4) = 43: 43+4*1^2 = 47, which is prime. 43+4*2^2 = 59, which is prime. 43+4*3^2 = 79, which is prime. 43+4*4^2 = 107, which is prime. 43+4*5^2 = 143 = 11*13, which is composite.
		

Links

• Carlos Rivera, Puzzle 464. p+4*x^2. [From _Jens Kruse Andersen_, Oct 24 2008]

Crossrefs

Cf. A000040 (the prime numbers), A023200 (primes p such that p + 4 is also prime), A049492 (primes p such that p + 4 and p + 16 are also prime), A092475 (primes p such that p + 4, p + 16 and p + 36 are also prime).

Extensions

Correction and a(11) - a(15) from Jens Kruse Andersen, Oct 24 2008

Edited by N. J. A. Sloane, Feb 08 2019, merging this with an essentially identical sequence submitted by Jon E. Schoenfield, Feb 02 2019