

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.


5



2, 19, 3, 277, 43, 53593, 7, 67, 37, 1483087, 1867783, 9671300983, 376040154163, 13491637509487, 604490757900187, 409333
(list;
graph;
refs;
listen;
history;
text;
internal format)



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



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).


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



