A375386 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.

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

Offset

2,2

Comments

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

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

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Example

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.

Maple

f:= proc(n) local s, i, m, dd, d, j;
  m:= 1;
  s:= ithprime(n);
  for i from n-1 to 1 by -1 do
    d:= s - ithprime(i);
    if s - m*d < 2 then return dd fi;
    for j from 2 while isprime(s-j*d) do od;
    if j > m then m:= j; dd:= d fi;
  od;
  dd
end proc:
map(f, [$2..100]);

Crossrefs

Cf. A000040, A373888.

Sequence in context: A124676 A076249 A062170 * A307536 A248842 A286538

Adjacent sequences: A375383 A375384 A375385 * A375387 A375388 A375389

Keyword

nonn,look

Author

Robert Israel, Aug 13 2024

Status

approved