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
Keywords
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
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
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