A198697 - OEIS

%I #24 Mar 08 2024 02:33:25

%S 4,4,6,6,6,6,8,4,14,6,10,10,4,6,10,6,14,14,10,8,8,10,10,6,8,12,8,12,

%T 18,10,10,12,12,10,10,8,8,14,12,10,4,14,14,20,10,14,8,12,6,10,10,10,

%U 18,8,22,10,10,12,12,18,6,6,12,34,18,14,8,12,4,12,8,8

%N Values of local maxima in differences of primes, A001223.

%H Robert Israel, <a href="/A198697/b198697.txt">Table of n, a(n) for n = 1..10000</a>

%H Zak Seidov, <a href="/A198697/a198697_1.png">A001223: maxima of 2nd order</a>

%p P:= select(isprime,[2,seq(i,i=3..1000,2)]):

%p DP:= P[2..-1] - P[1..-2]:

%p J:= select(t -> DP[t] > DP[t-1] and DP[t] > DP[t+1], [$2..nops(DP)-1]):

%p DP[J]; # _Robert Israel_, Mar 07 2024

%t nn = 1001; t = Differences[Prime[Range[nn]]]; t2 = {}; Do[If[t[[n - 1]] < t[[n]] && t[[n]] > t[[n + 1]], AppendTo[t2, {n, t[[n]]}]], {n, 2, nn - 2}]; Transpose[t2][[2]] (* _T. D. Noe_, Dec 27 2011 *)

%t Select[Partition[Differences[Prime[Range[400]]],3,1],#[[1]]<#[[2]]>#[[3]]&][[;;,2]] (* _Harvey P. Dale_, Mar 07 2023 *)

%Y Cf. A198696 (positions of local maxima in A001223).

%Y Cf. A196175 (positions of local minima in A001223).

%Y Cf. A001223 (first differences of primes).

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 29 2011