cp's OEIS Frontend

A088426 Number of primes in arithmetic progression starting with 19 and with d=2n.

%I A088426 #22 May 31 2022 12:51:27
%S A088426 1,2,1,1,2,3,1,1,2,1,2,3,1,2,1,1,2,1,1,2,3,1,1,2,1,2,4,1,1,4,1,2,1,1,
%T A088426 2,1,1,1,2,1,2,2,1,2,3,1,2,1,1,1,1,1,1,2,1,2,1,1,2,2,1,1,1,1,2,3,1,1,
%U A088426 2,1,1,3,1,2,1,1,2,1,1,2,2,1,1,1,1,2,4,1,2,3,1,1,1,1,1,2,1,1,1,1
%N A088426 Number of primes in arithmetic progression starting with 19 and with d=2n.
%C A088426 Arithmetic progression is stopped when next term is not prime. E.g. for n=6 (d=12), a=3, that is 19,31,43 are prime, while next term, 55, is not prime.
%C A088426 From _Robert Israel_, Jul 27 2020: (Start)
%C A088426 a(n) = 1 if n == 1 (mod 3), a(n) <= 2 if n == 2 (mod 3).
%C A088426 If a(n) >= p where p is 3, 5, 7, 11, 13 or 17, then n is divisible by p.
%C A088426 All a(n) < 19.
%C A088426 Records:
%C A088426 a(1)=1
%C A088426 a(2)=2
%C A088426 a(6)=3
%C A088426 a(27)=4
%C A088426 a(210)=5
%C A088426 a(825)=6
%C A088426 a(16380)=7
%C A088426 a(273420)=9
%C A088426 a(17853675)=10 (End)
%C A088426 From _David A. Corneth_, Jul 29 2020: (Start)
%C A088426 Other first occurrences are:
%C A088426 a(779520) = 8
%C A088426 a(4918073160) = 11
%C A088426 a(3187366788375) = 12
%C A088426 a(6125952702870) = 13
%C A088426 If a(k) = 14 then k > 4.8*10^15.
%C A088426 If a(k) = 15 then k > 1.77 * 10^16. (End)
%H A088426 Robert Israel, <a href="/A088426/b088426.txt">Table of n, a(n) for n = 1..10000</a>
%p A088426 f:= proc(n) local d,k;
%p A088426   d:= 2*n;
%p A088426   for k from 1 while isprime(19+d*k) do od:
%p A088426   k
%p A088426 end proc:
%p A088426 map(f, [$1..200]); # _Robert Israel_, Jul 27 2020
%t A088426 bb={}; Do[s=1; Do[If[PrimeQ[19+k*d], s=s+1, bb={bb, s}; Break[]], {k, 10}], {d, 2, 200, 2}]; Flatten[bb]
%Y A088426 Cf. A005115, A088420, A088421, A088422, A088423, A088424, A088425, A088427, A088428, A088429.
%K A088426 easy,nonn
%O A088426 1,2
%A A088426 _Zak Seidov_, Sep 29 2003