The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A166594

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A166594

Maximal prime gap q-p encountered from 0 to least prime > n.
(history; published version)

#21 by Michael De Vlieger at Sat Jun 10 08:10:43 EDT 2023

STATUS

proposed

approved

#20 by Michel Marcus at Thu Jun 08 03:16:33 EDT 2023

STATUS

editing

proposed

#19 by Michel Marcus at Thu Jun 08 03:15:27 EDT 2023

CROSSREFS

Cf. A002386, A063095, A151800, A166597, A327441.

Discussion

Thu Jun 08

03:16

Michel Marcus: I wrote a script but found A327441; I must have misunderstood name ?

#18 by Michel Marcus at Thu Jun 08 03:08:28 EDT 2023

REFERENCES

Maier, Helmut, and Carl Pomerance. "Unusually large gaps between consecutive primes." Transactions of the American Mathematical Society 322.1 (1990): 201-237.

LINKS

Helmut Maier and Carl Pomerance, <a href="https://doi.org/10.1090/S0002-9947-1990-0972703-X">Unusually large gaps between consecutive primes</a>, Transactions of the American Mathematical Society 322.1 (1990): 201-237.

STATUS

approved

editing

#17 by N. J. A. Sloane at Sat Feb 22 20:54:24 EST 2020

EXAMPLE

a(0) = 2 since the least prime greater than 0 is 2 (first occurence occurrence of gap 2).

a(7) = 4 since the least prime greater than 7 is 11 (first occurence occurrence of gap 4).

Discussion

Sat Feb 22

20:54

OEIS Server: https://oeis.org/edit/global/2851

#16 by N. J. A. Sloane at Wed Sep 11 15:38:25 EDT 2019

STATUS

editing

approved

#15 by N. J. A. Sloane at Wed Sep 11 15:38:23 EDT 2019

REFERENCES

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, 1996, Section VII.22, p. 249. (See G(x). Gives bounds.)

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

STATUS

approved

editing

#14 by N. J. A. Sloane at Wed Sep 11 15:03:43 EDT 2019

STATUS

editing

approved

#13 by N. J. A. Sloane at Wed Sep 11 15:03:42 EDT 2019

MAPLE

a:=[op(a), r]; od: a; # N. J. A. Sloane, Sep 11 2019

STATUS

approved

editing

#12 by N. J. A. Sloane at Wed Sep 11 15:03:14 EDT 2019

STATUS

editing

approved