A088426 - OEIS

%I #22 May 31 2022 12:51:27

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

%C 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 From _Robert Israel_, Jul 27 2020: (Start)

%C a(n) = 1 if n == 1 (mod 3), a(n) <= 2 if n == 2 (mod 3).

%C If a(n) >= p where p is 3, 5, 7, 11, 13 or 17, then n is divisible by p.

%C All a(n) < 19.

%C Records:

%C a(1)=1

%C a(2)=2

%C a(6)=3

%C a(27)=4

%C a(210)=5

%C a(825)=6

%C a(16380)=7

%C a(273420)=9

%C a(17853675)=10 (End)

%C From _David A. Corneth_, Jul 29 2020: (Start)

%C Other first occurrences are:

%C a(779520) = 8

%C a(4918073160) = 11

%C a(3187366788375) = 12

%C a(6125952702870) = 13

%C If a(k) = 14 then k > 4.8*10^15.

%C If a(k) = 15 then k > 1.77 * 10^16. (End)

%H Robert Israel, <a href="/A088426/b088426.txt">Table of n, a(n) for n = 1..10000</a>

%p f:= proc(n) local d,k;

%p   d:= 2*n;

%p   for k from 1 while isprime(19+d*k) do od:

%p   k

%p end proc:

%p map(f, [$1..200]); # _Robert Israel_, Jul 27 2020

%t 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 Cf. A005115, A088420, A088421, A088422, A088423, A088424, A088425, A088427, A088428, A088429.

%K easy,nonn

%O 1,2

%A _Zak Seidov_, Sep 29 2003