

A053695


Differences between record prime gaps.


10



1, 2, 2, 2, 6, 4, 2, 2, 12, 2, 8, 8, 20, 14, 10, 16, 2, 4, 14, 16, 6, 26, 30, 10, 2, 12, 14, 2, 32, 6, 4, 28, 16, 18, 28, 2, 10, 62, 8, 4, 6, 12, 4, 10, 14, 2, 16, 2, 6, 42, 6, 14, 50, 22, 42, 50, 12, 26, 2, 100, 10, 8, 208, 52, 14, 22, 4, 24, 24, 56, 28, 14, 72, 34, 12, 22, 16, 4, 20
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The largest known term of this sequence is a(63) = 1132  924 = 208. This seems rather strange for a(63) > 2*100+7 where 100 = max {a(k) k < 63}. {1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,42,50,52,56,62,72,100,208} is the set of the distinct first 75 terms of the sequence. What is the smallest number m such that a(m) = 36?  Farideh Firoozbakht, May 30 2014
Conjecture: a(n) <= A005250(n). Based on the equivalent statement at A005250: A005250(n+1) / A005250(n) <= 2.  John W. Nicholson, Dec 30 2015
Does the number 2 appear infinitely many times in this sequence?  Elizabeth Axoy, Jul 21 2019


LINKS

Table of n, a(n) for n=1..79.
Alexei Kourbatov, On the nth record gap between primes in an arithmetic progression. International Mathematical Forum, Vol. 13, 2018, No. 2, 6578, arXiv:1709.05508v3 [math.NT].
Eric Weisstein's World of Mathematics, Prime Gaps
Wikipedia, Prime gap


FORMULA

a(n) = A005250(n+1)  A005250(n).
A005250(n+1) = 1 + Sum_{i=1..n} a(i).  John W. Nicholson, Dec 29 2015


CROSSREFS

Cf. A000101, A001223, A002386, A005250, A053686, A309282, A309283.
Sequence in context: A126615 A158524 A054274 * A210550 A208659 A209752
Adjacent sequences: A053692 A053693 A053694 * A053696 A053697 A053698


KEYWORD

nonn,nice,hard


AUTHOR

Jeff Burch, Mar 23 2000


EXTENSIONS

Missing term 1 and more terms added by Farideh Firoozbakht, May 30 2014
a(75)a(76) from John W. Nicholson, Feb 27 2018
a(77)a(79) added by Elizabeth Axoy, Jul 21 2019


STATUS

approved



