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A327441
a(n) = max_{p <= n} (p'-p), where p and p' are successive primes.
4
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, 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, 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
OFFSET
2,2
COMMENTS
This is Maier and Pomerance's G(n).
REFERENCES
Erdos, Paul. "On the difference of consecutive primes." The Quarterly Journal of Mathematics 1 (1935): 124-128.
Erdös, P. "On the difference of consecutive primes." Bulletin of the American Mathematical Society 54.10 (1948): 885-889.
Maier, Helmut, and Carl Pomerance. "Unusually large gaps between consecutive primes." Transactions of the American Mathematical Society 322.1 (1990): 201-237.
D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.22, p. 249. (See G(x). Gives bounds.)
Rankin, Robert Alexander. "The difference between consecutive prime numbers V." Proceedings of the Edinburgh Mathematical Society 13.4 (1963): 331-332.
LINKS
EXAMPLE
a(2) = 1 from p=2, p'=3.
a(3) = 2 from p=3, p'=5.
MAPLE
with(numtheory);
M:=120; a:=[]; r:=0;
for x from 2 to M do
i1:=pi(x); p:=ithprime(i1); q:=ithprime(i1+1); d:=q-p;
if d>r then r:=d; fi;
a:=[op(a), r]; od: a; # N. J. A. Sloane, Sep 11 2019
CROSSREFS
Cf. A063095.
A166594 is a similar sequence, but the present sequence matches the definition used by Maier and Pomerance.
Sequence in context: A080217 A157901 A350697 * A335855 A297824 A281796
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 11 2019
STATUS
approved