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

0,1

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]

Links

Table of n, a(n) for n=0..15.

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

Example

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.

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).

Sequence in context: A221602 A354207 A358980 * A059706 A128361 A096481

Adjacent sequences: A092117 A092118 A092119 * A092121 A092122 A092123

Keyword

nonn

Author

Ray G. Opao, Mar 29 2004

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

Status

approved