OFFSET
1,1
COMMENTS
Differences k - s: 6, 9, 77, 15, 21, 91, 4, 33, 69, 25, ... with minimal value 4.
What about the maximal value of k - s?
k-s is unbounded, because the gaps between semiprimes are unbounded. In fact, given any n distinct primes, by the Chinese Remainder Theorem there exist n consecutive positive integers that are each divisible by the cube of one of these primes (and thus not semiprimes). - Robert Israel, Dec 27 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
s=4, k=10, 6 and 14 are all semiprimes,
s=6, k=15, 9 and 21 are all semiprimes,
s=9, k=86, 77 and 95 are all semiprimes.
MAPLE
N:= 10^3:
SP:= select(t -> numtheory:-bigomega(t)=2, [$4..N]):
f:= proc(n) local i, s;
s:= SP[n];
for i from n+1 do
if numtheory:-bigomega(SP[i]-s)=2 and numtheory:-bigomega(SP[i]+s)=2 then return SP[i] fi
od;
end proc:
map(f, [$1..100]); # Robert Israel, Dec 27 2020
PROG
(PARI) issemip(n) = bigomega(n)==2;
lista(nn) = {my(v = select(issemip, [1..nn])); for (n=1, #v, my(ik=n+1, s=v[n]); while (!(issemip(v[ik]+s) && issemip(v[ik]-s)), ik++; if (ik>#v, return)); print1(v[ik], ", "); ); } \\ Michel Marcus, Dec 19 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Dec 17 2020
STATUS
approved