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A118777 a(0) = 1; n > 0: a(n) = a(n-1) + d, d = -/+1 if n is prime/nonprime. 2

%I #21 Nov 01 2021 12:20:38

%S 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,

%T 11,12,13,14,15,14,15,16,17,16,17,16,17,18,19,18,19,20,21,22,23,22,23,

%U 24,25,26,27,26,27,26,27,28,29,30,31,30,31,32,33,32,33,32,33,34,35,36

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

%H Antti Karttunen, <a href="/A118777/b118777.txt">Table of n, a(n) for n = 0..10000</a>

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

%F From _Antti Karttunen_, Aug 21 2016: (Start)

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

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

%F (End)

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

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

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

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

%o ;; _Antti Karttunen_, Aug 19 2016

%Y Cf. A000720, A010051.

%Y One more than A097454, two more than A072731.

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

%K nonn

%O 0,2

%A _Zak Seidov_, May 22 2006

%E Offset and the name corrected by _Antti Karttunen_, Aug 19 2016

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)