A375386 - OEIS

%I #8 Aug 14 2024 08:33:53

%S 1,2,2,4,2,6,6,6,6,12,6,12,12,18,12,6,24,24,12,6,6,12,18,18,30,30,18,

%T 6,30,30,30,24,36,48,24,30,12,18,42,6,54,54,42,48,60,30,42,30,66,42,

%U 66,30,60,30,12,6,30,48,84,60,60,78,60,102,60,60,30,78,36,60,90,18,90,6,72,96,30,54

%N a(n) is the common difference in the longest arithmetic progression of primes ending in prime(n).  If there is more than one such arithmetic progression, the smallest difference is chosen.

%C a(n) is the smallest common difference in an arithmetic progression of A373888(n) primes ending in prime(n).

%C a(n) is divisible by all primes < min(A373888(n) + 1, prime(n) - (A373888(n)-1)*a(n)).

%H Robert Israel, <a href="/A375386/b375386.txt">Table of n, a(n) for n = 2..10000</a>

%e a(4) = 2 because the 4th prime is 7 and the arithmetic progression of 3 primes ending in 7, namely 3, 5, 7, has common difference 2.

%p f:= proc(n) local s, i, m, dd, d, j;

%p   m:= 1;

%p   s:= ithprime(n);

%p   for i from n-1 to 1 by -1 do

%p     d:= s - ithprime(i);

%p     if s - m*d < 2 then return dd fi;

%p     for j from 2 while isprime(s-j*d) do od;

%p     if j > m then m:= j; dd:= d fi;

%p   od;

%p   dd

%p end proc:

%p map(f, [$2..100]);

%Y Cf. A000040, A373888.

%K nonn,look

%O 2,2

%A _Robert Israel_, Aug 13 2024