A118777 a(0) = 1; n > 0: a(n) = a(n-1) + d, d = +-1 if n is prime/nonprime.

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

Offset: 0

Author

Zak Seidov, May 22 2006

Keywords

• nonn

Links

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

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.

Programs

Mathematica

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

Scheme

;; With memoization-macro definec.
(definec (A118777 n) (if (zero? n) 1 (+ (A118777 (- n 1)) (expt -1 (A010051 n)))))
;; Antti Karttunen, Aug 19 2016

Scheme

(define (A118777 n) (+ 1 (- n (* 2 (A000720 n))))) ;; After formula given by the original author.
;; Antti Karttunen, Aug 19 2016

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)

Extensions

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