|
%I #26 Jun 30 2022 08:51:32
%S 3,2,17,347,2903,15373,128981,1319407,17797517,94097537,6927837557,
%T 48486712783,968068681511,1472840004017,129001208165717
%N First primes followed by sequences of exactly n monotonic increasing prime gaps.
%C For n > 1, a(n) is the prime preceding A229832(n-1). [Follows from the definitions] - _Chris Boyd_, Mar 28 2015
%C Banks, Freiberg, & Turnage-Butterbaugh show that a(n) exists for each n. - _Charles R Greathouse IV_, Jun 30 2022
%H William D. Banks, Tristan Freiberg, and Caroline L. Turnage-Butterbaugh, <a href="https://arxiv.org/abs/1311.7003">Consecutive primes in tuples</a> (2013), arXiv:1311.7003 [math.NT].
%H Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_011.htm">Puzzle 11. Distinct, Increasing & Decreasing Gaps</a>, The Prime Puzzles and Problems Connection.
%e a(8)=1319407 is the first prime to be followed by n=8 monotonic increasing prime gaps: 4,8,10,14,16,18,32,34.
%e a(14)=1472840004017 is the first prime to be followed by n=14 monotonic increasing prime gaps: 2,4,6,8,10,12,14,28,30,38,48,64,66,74.
%o (PARI) is(p,k,g=0)=my(q=nextprime(p+1));if(g>=q-p,0,if(k>1,is(q,k-1,q-p),q-p>=nextprime(q+1)-q))
%o a(n)=forprime(p=2,,if(is(p,n),return(p))) \\ _Charles R Greathouse IV_, Nov 02 2012
%Y Cf. A158940 (monotonic decreasing prime gaps), A229832.
%Y Cf. A133697.
%K more,nonn
%O 1,1
%A Alan Worley (aw(AT)xiboo.co.uk), Mar 31 2009
%E a(15) from _Giovanni Resta_, Apr 19 2016
|
