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A069754 Counts transitions between prime and composite to reach the number n. 6
0, 1, 1, 2, 3, 4, 5, 6, 6, 6, 7, 8, 9, 10, 10, 10, 11, 12, 13, 14, 14, 14, 15, 16, 16, 16, 16, 16, 17, 18, 19, 20, 20, 20, 20, 20, 21, 22, 22, 22, 23, 24, 25, 26, 26, 26, 27, 28, 28, 28, 28, 28, 29, 30, 30, 30, 30, 30, 31, 32, 33, 34, 34, 34, 34, 34, 35, 36, 36, 36, 37, 38, 39 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

The following sequences all appear to have the same parity (with an extra zero term at the start of A010051): A010051, A061007, A035026, A069754, A071574. - Jeremy Gardiner, Aug 09 2002

For n > 2: a(n) = 2*A000720(n) - 2 - A010051(n). - Reinhard Zumkeller, Dec 04 2012

LINKS

T. D. Noe, Table of n, a(n) for n=1..1000

FORMULA

When n is prime, a(n) = 2 pi(n) - 3. When n is composite, a(n) = 2 pi(n) - 2. pi(n) is the prime counting function A000720.

EXAMPLE

a(6)=4 because there are 4 transitions: 1 to 2, 3 to 4, 4 to 5 and 5 to 6

MATHEMATICA

For[lst={0}; trans=0; n=2, n<100, n++, If[PrimeQ[n]!=PrimeQ[n-1], trans++ ]; AppendTo[lst, trans]]; lst

pts[n_]:=Module[{c=2PrimePi[n]}, If[PrimeQ[n], c-3, c-2]]; Join[{0, 1}, Array[ pts, 80, 3]] (* Harvey P. Dale, Nov 12 2011 *)

Accumulate[If[Sort[PrimeQ[#]]=={False, True}, 1, 0]&/@Partition[ Range[ 0, 80], 2, 1]] (* Harvey P. Dale, May 06 2013 *)

PROG

(Haskell)

a069754 1 = 0

a069754 2 = 1

a069754 n = 2 * a000720 n - 2 - (toInteger $ a010051 $ toInteger n)

-- Reinhard Zumkeller, Dec 04 2012

CROSSREFS

Cf. A000720.

Cf. A211005 (run lengths).

Sequence in context: A102674 A097623 A198462 * A097622 A236561 A110010

Adjacent sequences:  A069751 A069752 A069753 * A069755 A069756 A069757

KEYWORD

easy,nice,nonn

AUTHOR

T. D. Noe, May 02 2002

STATUS

approved

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Last modified December 9 02:36 EST 2016. Contains 278959 sequences.