

A053695


Differences between record prime gaps.


7



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
(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


LINKS



FORMULA



MATHEMATICA

m = 2; r = 0; Differences@ Reap[Monitor[Do[If[Set[d, Set[n, NextPrime[m]]  m] > r, Set[r, d]; Sow[d]]; m = n, {i, 10^7}], i]][[1, 1]] (* Michael De Vlieger, Oct 30 2021 *)


CROSSREFS



KEYWORD

nonn,nice,hard,changed


AUTHOR



EXTENSIONS



STATUS

approved



