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A375511
a(n) is the common difference in the longest arithmetic progression of semiprimes ending in the n-th semiprime. If there is more than one such arithmetic progression, the smallest difference is chosen.
2
2, 3, 1, 4, 1, 6, 8, 3, 11, 12, 12, 1, 12, 1, 12, 14, 13, 17, 11, 12, 24, 7, 18, 35, 19, 24, 8, 24, 18, 29, 8, 36, 1, 24, 17, 30, 12, 4, 3, 48, 4, 36, 11, 48, 23, 24, 1, 30, 12, 13, 12, 36, 42, 24, 14, 16, 36, 14, 8, 32, 36, 7, 60, 42, 60, 60, 3, 4, 36, 46, 4, 12, 32, 4, 60, 16, 18, 44, 36, 16
OFFSET
2,1
COMMENTS
a(n) is the smallest common difference in an arithmetic progression of A373887(n) semiprimes ending in A001358(n).
LINKS
EXAMPLE
The 5th semiprime is 14, A373887(5) = 3, and there are two arithmetic progressions of semiprimes of length 3 ending in 14, namely 6, 10, 14 with common difference 4 and 4, 9, 14 with common difference 5. Therefore a(5) = min(4, 5) = 4.
MAPLE
S:= select(t -> numtheory:-bigomega(t)=2, [$1..10^5]):
f:= proc(n) local s, i, m, d, j, dm;
m:= 1;
s:= S[n];
for i from n-1 to 1 by -1 do
d:= s - S[i];
if s - m*d < 4 then return dm fi;
for j from 2 while ListTools:-BinarySearch(S, s-j*d) <> 0 do od;
if j > m then m:= j; dm:= d fi;
od;
dm;
end proc:
map(f, [$2..200]);
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert Israel, Aug 18 2024
STATUS
approved