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Least prime which is followed by a gap of 30n
1

%I #11 Oct 28 2021 12:37:08

%S 4297,43331,404851,1895359,13626257,17051707,20831323,391995431,

%T 1391048047,4758958741,6291356009,20068818197,53241805651,82490815123,

%U 63816175447,482423533897,2209016910131,738832927927,4442109925217,4872634110067,12644461143649,10653514291843,15712145060693,111113196467011

%N Least prime which is followed by a gap of 30n

%C Data up to 2e9 computed independently and (up to 391995431) double-checked with A140791. Data beyond 2e9 taken from Nicely's web page (which would yield further terms, at least up to a(47) - notice that the "?" in column 10, e.g. for gap 1440, indicates that the listed values is the first *known*, but maybe not the first occurrence). See there for credits.

%H Thomas R. Nicely, <a href="https://faculty.lynchburg.edu/~nicely/gaps/gaplist.html">First occurrence prime gaps</a> [For local copy see A000101]

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>.

%F a(n) = A000230(15n) = A058193(5n) = A140791(3n)

%o (PARI) o=2;g=30;forprime(p=3,,(o+g != o=p) & next; print1(p-g",");g+=30) \\ Warning: this code assumes that the sequence is increasing, which may not be the case. - _M. F. Hasler_, Apr 09 2013

%K nonn,hard

%O 1,1

%A _M. F. Hasler_, Apr 09 2013