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

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, 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, 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

Offset

1,2

Comments

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.

From Robert Israel, Jul 27 2020: (Start)

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

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

All a(n) < 19.

Records:

a(1)=1

a(2)=2

a(6)=3

a(27)=4

a(210)=5

a(825)=6

a(16380)=7

a(273420)=9

a(17853675)=10 (End)

From David A. Corneth, Jul 29 2020: (Start)

Other first occurrences are:

a(779520) = 8

a(4918073160) = 11

a(3187366788375) = 12

a(6125952702870) = 13

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

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

f:= proc(n) local d, k;
  d:= 2*n;
  for k from 1 while isprime(19+d*k) do od:
  k
end proc:
map(f, [$1..200]); # Robert Israel, Jul 27 2020

Mathematica

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]

Crossrefs

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

Sequence in context: A333765 A088198 A318288 * A124769 A176484 A144328

Adjacent sequences: A088423 A088424 A088425 * A088427 A088428 A088429

Keyword

easy,nonn

Author

Zak Seidov, Sep 29 2003

Status

approved