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A118777 a(0) = 1; n > 0: a(n) = a(n-1) + d, d = -/+1 if n is prime/nonprime. 2
1, 2, 1, 0, 1, 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 10, 11, 10, 11, 10, 11, 12, 13, 14, 15, 14, 15, 16, 17, 16, 17, 16, 17, 18, 19, 18, 19, 20, 21, 22, 23, 22, 23, 24, 25, 26, 27, 26, 27, 26, 27, 28, 29, 30, 31, 30, 31, 32, 33, 32, 33, 32, 33, 34, 35, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = n + 1 - 2*primepi(n), n = 0, 1, 2, ..., where primepi(n) = A000720(n).

From Antti Karttunen, Aug 21 2016: (Start)

a(0) = 1, for n >= 1, a(n) = a(n-1) + (-1)^A010051(n). (from the definition).

For all n >= 1, a(n) = 1+A097454(n) = 2+A072731(n).

(End)

MATHEMATICA

(*1*) a=1; s={a}; Do[b=a+If[PrimeQ[n], -1, 1]; AppendTo[s, b]; a=b, {n, 100}]; s

(*2*) Table[n + 1 - 2*PrimePi[n], {n, 0, 100}]

PROG

(Scheme, two versions, the first defined with memoization-macro definec)

(definec (A118777 n) (if (zero? n) 1 (+ (A118777 (- n 1)) (expt -1 (A010051 n)))))

(define (A118777 n) (+ 1 (- n (* 2 (A000720 n))))) ;; After formula given by the original author.

;; Antti Karttunen, Aug 19 2016

CROSSREFS

Cf. A000720, A010051.

One more than A097454, two more than A072731.

For no apparent reason, the terms a(3)..a(24) are equal to the terms a(0)..a(21) of A276090.

Sequence in context: A317754 A317854 A317742 * A073068 A166006 A330935

Adjacent sequences:  A118774 A118775 A118776 * A118778 A118779 A118780

KEYWORD

nonn

AUTHOR

Zak Seidov, May 22 2006

EXTENSIONS

Offset and the name corrected by Antti Karttunen, Aug 19 2016

STATUS

approved

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Last modified June 20 08:30 EDT 2021. Contains 345162 sequences. (Running on oeis4.)