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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.
4
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
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
Sequence in context: A124676 A076249 A062170 * A307536 A248842 A286538
KEYWORD
nonn,look
AUTHOR
Robert Israel, Aug 13 2024
STATUS
approved