cp's OEIS Frontend

A358482 a(n) is the first prime p such that, if q is the next prime, (p*q+p+q)/5^n is a prime.

%I A358482 #63 Dec 30 2022 06:32:40
%S A358482 2,7,1847,90793,139313,1790293,3834043,5521543,24996487,2062865293,
%T A358482 5555052793,12111965183,95460776921,6045070151921,10204150316653,
%U A358482 70501997496487,442748358250633,368313674465183,2935956099058987,10360552690003447,120999670013476223,1820610211470152737
%N A358482 a(n) is the first prime p such that, if q is the next prime, (p*q+p+q)/5^n is a prime.
%C A358482 Suggested in an email by _J. M. Bergot_.
%C A358482 For n >= 1, a(n) has the form k * 5^n + x, for some k >= 0, where x is a solution to the modular quadratic equation x^2 + (d+2)*x + d == 0 (mod 5^n), where d = q-p. - _Daniel Suteu_, Dec 28 2022
%e A358482 a(2) = 1847 because 1847 is prime, the next prime is 1861, 1847*1861 + 1847 + 1861 = 3440975 = 5^2 * 137639 where 137639 is prime, and no smaller prime works.
%p A358482 V:= Array(0..8):
%p A358482 q:= 2: count:= 0:
%p A358482 while count < 9 do
%p A358482   p:= q; q:= nextprime(q);
%p A358482 t:= p*q+p+q;
%p A358482 k:= padic:-ordp(t,5);
%p A358482 if V[k] = 0 and isprime(t/5^k) then
%p A358482   V[k]:= p; count:= count+1
%p A358482 fi
%p A358482 od:
%p A358482 convert(V,list);
%Y A358482 Cf. A000351, A002386, A126148.
%K A358482 nonn
%O A358482 0,1
%A A358482 _Robert Israel_, Dec 25 2022
%E A358482 a(11) from _Michael S. Branicky_, Dec 26 2022
%E A358482 a(12)-a(15) from _David A. Corneth_, Dec 26 2022
%E A358482 a(16) from _Martin Ehrenstein_, Dec 27 2022
%E A358482 a(17)-a(21) from _Daniel Suteu_, Dec 28 2022