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A088426
Number of primes in arithmetic progression starting with 19 and with d=2n.
10
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
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]
KEYWORD
easy,nonn
AUTHOR
Zak Seidov, Sep 29 2003
STATUS
approved