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%I #15 Sep 11 2019 15:51:38
%S 1,2,2,2,2,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,6,6,6,6,6,6,6,6,6,6,6,6,6,
%T 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,
%U 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,14,14,14,14,14,14,14
%N a(n) = max_{p <= n} (p'-p), where p and p' are successive primes.
%C This is Maier and Pomerance's G(n).
%D Erdos, Paul. "On the difference of consecutive primes." The Quarterly Journal of Mathematics 1 (1935): 124-128.
%D Erdös, P. "On the difference of consecutive primes." Bulletin of the American Mathematical Society 54.10 (1948): 885-889.
%D Maier, Helmut, and Carl Pomerance. "Unusually large gaps between consecutive primes." Transactions of the American Mathematical Society 322.1 (1990): 201-237.
%D D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.22, p. 249. (See G(x). Gives bounds.)
%D Rankin, Robert Alexander. "The difference between consecutive prime numbers V." Proceedings of the Edinburgh Mathematical Society 13.4 (1963): 331-332.
%H N. J. A. Sloane, <a href="/A327441/b327441.txt">Table of n, a(n) for n = 2..20000</a>
%e a(2) = 1 from p=2, p'=3.
%e a(3) = 2 from p=3, p'=5.
%p with(numtheory);
%p M:=120; a:=[]; r:=0;
%p for x from 2 to M do
%p i1:=pi(x); p:=ithprime(i1); q:=ithprime(i1+1); d:=q-p;
%p if d>r then r:=d; fi;
%p a:=[op(a),r]; od: a; # _N. J. A. Sloane_, Sep 11 2019
%Y Cf. A063095.
%Y A166594 is a similar sequence, but the present sequence matches the definition used by Maier and Pomerance.
%K nonn
%O 2,2
%A _N. J. A. Sloane_, Sep 11 2019
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