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First primes followed by sequences of exactly n monotonic decreasing prime gaps.
2

%I #7 Jun 30 2022 14:51:13

%S 2,7,31,1637,1831,74653,322171,5051309,11938793,245333213,245333159,

%T 130272314561,1273135176799,23840790158827

%N First primes followed by sequences of exactly n monotonic decreasing prime gaps.

%C a(15) > 1.3*10^14. - _Giovanni Resta_, Apr 19 2016

%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].

%e a(4)=1637 is the first prime to be followed by n=4 monotonic decreasing prime gaps: 20,6,4,2.

%e a(13)=1273135176799 is the first prime to be followed by n=13 monotonic decreasing prime gaps: 72,60,46,44,42,36,34,24,12,8,6,4,2.

%Y Cf. A158939 (monotonic increasing prime gaps)

%K more,nonn

%O 1,1

%A Alan Worley (aw(AT)xiboo.co.uk), Mar 31 2009

%E a(14) from _Giovanni Resta_, Apr 19 2016