%I #17 Oct 30 2021 13:43:36
%S 1,2,3,4,7,9,10,11,17,18,22,26,36,43,48,56,57,59,66,74,77,90,105,110,
%T 111,117,124,125,141,144,146,160,168,177,191,192,197,228,232,234,237,
%U 243,245,250,257,258,266,267,270,291,294,301,326,337,358,383,389,402,403,453,458,462,566,592,599,610,612,624,636,664,678,685,721,738,744,755,763,765,775
%N Half of increasing gaps between primes.
%C The primes in this sequence are 2, 3, 7, 11, 17, 43, 59, 191, 197, 257, ...
%C The squares are 1, 4, 9, 36, 144,...
%F a(n) = A005250(n)/2 for n>1.
%t max = 10^7; Module[{d = Differences[Prime[Range[max]]], ls = {2}}, Table[If[d[[n]] > Last[ls], AppendTo[ls, d[[n]]]], {n, max - 1}]; ls/2]
%Y Cf. A005250.
%K nonn
%O 2,2
%A _Michel Lagneau_, Mar 22 2016
%E a(55)-a(80) using b-file of A005250 by _Hugo Pfoertner_, Oct 30 2021