cp's OEIS Frontend

A090688 First occurrence of primes in the progression k*x^2-1.

%I A090688 #17 Aug 25 2024 18:45:28
%S A090688 3,7,2,3,19,5,251,7,89,43,11,467,13,59,67,17,683,19,83,197,367,23,103,
%T A090688 107,251,463,29,4463,31,131,1223,139,11987,37,7643,359,163,41,13931,
%U A090688 43,179,33533,751,47,199,5099,467,211,53,1979,223,227,521,23599,59,8783,61
%N A090688 First occurrence of primes in the progression k*x^2-1.
%C A090688 It appears that the generating function k*x^2-1 will produce all primes eventually with some repetitions.
%C A090688 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 A090688 Robert Israel, <a href="/A090688/b090688.txt">Table of n, a(n) for n = 1..10000</a>
%F A090688 If p>=5 is prime, a(p+3-floor(sqrt(p)))=p. - _Robert Israel_, Nov 22 2020
%p A090688 f:= proc(k) local x;
%p A090688   if issqr(k) then return NULL fi;
%p A090688   for x from 1 do if isprime(k*x^2-1) then return k*x^2-1 fi od
%p A090688 end proc:
%p A090688 f(1):= 3: f(4):= 3:
%p A090688 map(f, [$1..300]); # _Robert Israel_, Nov 22 2020
%K A090688 easy,nonn
%O A090688 1,1
%A A090688 _Cino Hilliard_, Dec 18 2003