cp's OEIS Frontend

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.

%I A092120 #9 Feb 08 2019 12:30:38
%S A092120 2,19,3,277,43,53593,7,67,37,1483087,1867783,9671300983,376040154163,
%T A092120 13491637509487,604490757900187,409333
%N 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.
%C A092120 Similar to A092474 except that a(n)+4m^2 is composite for m = n+1.
%C A092120 a(19)=163. All other terms after a(15) are greater than 10^17 (if they exist). [From _Jens Kruse Andersen_, Oct 24 2008]
%H A092120 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_461.htm">Puzzle 464. p+4*x^2</a>. [From _Jens Kruse Andersen_, Oct 24 2008]
%e A092120 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.
%e A092120 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.
%Y A092120 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).
%K A092120 nonn
%O A092120 0,1
%A A092120 _Ray G. Opao_, Mar 29 2004
%E A092120 Correction and a(11) - a(15) from _Jens Kruse Andersen_, Oct 24 2008
%E A092120 Edited by _N. J. A. Sloane_, Feb 08 2019, merging this with an essentially identical sequence submitted by _Jon E. Schoenfield_, Feb 02 2019