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A195465
The first a(n) n-gap primes are lessers of twin primes, a(n) maximal.
1
0, 5, 5, 17, 5, 6, 14, 6, 24, 75, 2, 4, 27, 11, 48, 50, 46, 9, 21, 7, 16, 137, 4, 55, 85, 14, 111, 24, 102, 291, 67, 89, 155, 180, 137, 330, 127, 413, 250, 241, 332, 619, 139, 234, 453, 929, 94, 160, 169, 22, 131, 434
OFFSET
1,2
COMMENTS
For definition of n-gap primes, see comment to A195270.
Conjecture: a(n)>0 for n>1. This conjecture is equivalent to the conjecture that all terms of A195325 are lessers of twin primes.
MAPLE
a:= proc(n) local i, p, q;
p, q:= 2, 3;
for i from 0 do
while nextprime(n*p) < (n*q) do
p, q:= q, nextprime(q)
od;
if not isprime(p+2) then return i fi;
p, q:= q, nextprime(q)
od
end:
seq(a(n), n=1..20); # Alois P. Heinz, Sep 20 2011
MATHEMATICA
a[n_] := a[n] = Module[{i, p = 2, q = 3}, For[i = 0, True, i++, While[NextPrime[n p] < n q, p = q; q = NextPrime[q]]; If[!PrimeQ[p+2], Return[i]]; p = q; q = NextPrime[q]]];
Array[a, 20] (* Jean-François Alcover, Nov 21 2020, after Alois P. Heinz *)
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Sep 19 2011
STATUS
approved