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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
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).
Sequence in context: A221602 A354207 A358980 * A059706 A370387 A128361
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