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First occurrence of primes in the progression k*x^2-1.
2

%I #17 Aug 25 2024 18:45:28

%S 3,7,2,3,19,5,251,7,89,43,11,467,13,59,67,17,683,19,83,197,367,23,103,

%T 107,251,463,29,4463,31,131,1223,139,11987,37,7643,359,163,41,13931,

%U 43,179,33533,751,47,199,5099,467,211,53,1979,223,227,521,23599,59,8783,61

%N First occurrence of primes in the progression k*x^2-1.

%C It appears that the generating function k*x^2-1 will produce all primes eventually with some repetitions.

%C If k>2 is a square, there is no entry corresponding to k*x^2-1. Bunyakovsky's conjecture implies that there are primes for all other k. - _Robert Israel_, Nov 22 2020

%H Robert Israel, <a href="/A090688/b090688.txt">Table of n, a(n) for n = 1..10000</a>

%F If p>=5 is prime, a(p+3-floor(sqrt(p)))=p. - _Robert Israel_, Nov 22 2020

%p f:= proc(k) local x;

%p if issqr(k) then return NULL fi;

%p for x from 1 do if isprime(k*x^2-1) then return k*x^2-1 fi od

%p end proc:

%p f(1):= 3: f(4):= 3:

%p map(f, [$1..300]); # _Robert Israel_, Nov 22 2020

%K easy,nonn

%O 1,1

%A _Cino Hilliard_, Dec 18 2003