login
A196175
Positions of local minima in A001223.
4
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.
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
KEYWORD
nonn
AUTHOR
Zak Seidov, Oct 27 2011
STATUS
approved