A196175 Positions of local minima in A001223.

5, 7, 10, 13, 17, 20, 22, 26, 28, 31, 33, 35, 38, 41, 43, 45, 49, 52, 57, 60, 64, 67, 69, 75, 78, 81, 83, 85, 89, 93, 95, 98, 100, 104, 109, 113, 116, 120, 122, 126, 131, 134, 136, 138, 140, 142, 144, 148, 152, 155, 159, 163, 167, 169

Offset

1,1

Comments

Or, numbers n such that A001223(n-1)>A001223(n)<A001223(n+1).

We start with A001223:

S1= 1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4.

Local minima are shown in brackets:

S2= 1, 2, 2, {4,2,4}, {4,2,4}, {6,2,6}, {4,2,4}, 6, {6,2,6}, {4,2,6}, {6,4,6}, 8, {4,2,4}, {4,2,4}, {14,4,6}, {6,2,10};

values of local minima are 2, 2, 2, 2, 2, 2, 4, 2, 2, 4, 2, and positions of local minima in A001223 give this sequence. Note that in the first and second brackets we take A001223(6)=4 twice. Also note that all 2's starting with A001223(5) and so on are local minima but there are many other local minima.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Zak Seidov, Crests and troughs in A001223

Example

n=5 A001223(4)=4, A001223(5)=2, A001223(6)=4, and A001223(5) is the local minimum;
n=38: A001223(38)=4 is the local minimum because A001223(37)=6 and A001223(39)=6 both > A001223(38).

Mathematica

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][[1]] (* T. D. Noe, Dec 27 2011 *)

Prog

(Haskell)
a196175 n = a196175_list !! (n-1)
a196175_list = map (+ 2) $ elemIndices True $
   zipWith (\x y -> x < 0 && y > 0) a036263_list $ tail a036263_list
-- Reinhard Zumkeller, Oct 29 2011

Crossrefs

Cf. A001223 (differences between consecutive primes).

Cf. A036263 (second differences of primes).

Sequence in context: A060873 A186542 A287444 * A112251 A089061 A093115

Adjacent sequences: A196172 A196173 A196174 * A196176 A196177 A196178

Keyword

nonn

Author

Zak Seidov, Oct 27 2011

Status

approved