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A352392
a(n) is the least prime prime(k) such that prime(k+n-1)^2 - prime(k)^2 + prime(i) for i=k..k+n-1 are consecutive primes.
0
2, 5, 5, 37, 3181, 641, 1157111, 181995731
OFFSET
1,1
COMMENTS
a(9) > 6*10^9.
EXAMPLE
For n=3, a(3) = 5 because 5, 7, 11 are consecutive primes and 11^2 - 5^2 + 5 = 101, 11^2 - 5^2 + 7 = 103, 11^2 - 5^2 + 11 = 107 are consecutive primes, and 5 is the first prime that works.
MAPLE
f:= proc(n) local Q, i, d;
Q:= Vector([0, seq(ithprime(i), i=1..n-1)]);
do
Q[1..n-1]:= Q[2..n];
Q[n]:= nextprime(Q[n]);
d:= Q[n]^2 - Q[1]^2;
if isprime(Q[1]+d) and andmap(i -> Q[i+1]+d = nextprime(Q[i]+d), [$1..n-1]) then return Q[1] fi
od
end proc:
map(f, [$1..8]);
CROSSREFS
Cf. A347531.
Sequence in context: A297446 A154918 A176862 * A176081 A271222 A073339
KEYWORD
nonn,more
AUTHOR
J. M. Bergot and Robert Israel, Mar 14 2022
STATUS
approved