A267084 a(n) = ceiling(A007504(n)/n) - floor(A007504(n)/n); a(n) is 0 if n divides the sum of first n primes, 1 otherwise.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

1

Comments

a(n) = 0 for n=1, 23, 53, 853, ... see A045345.

It is conjectured that there are infinitely many zeros, but that their density is zero.

Links

Antti Karttunen, Table of n, a(n) for n = 1..12000

Javier Cilleruelo and Florian Luca, On the sum of the first n primes, Q. J. Math. 59:4 (2008), 14 pp.

Index entries for characteristic functions

Formula

a(n) = A225804(n) - A060620(n).

Mathematica

Table[Ceiling[(Plus@@Prime[Range[n]])/n]-Floor[(Plus@@Prime[Range[n]])/n], {n, 100}]

Prog

(PARI)
up_to = 105
v007504 = vector(up_to, i, prime(i));
for(i=2, up_to, v007504[i] = v007504[i-1]+v007504[i]); \\ Taking partial sums of primes here.
A007504(n) = v007504[n];
A267084(n) = if(!(A007504(n)%n), 0, 1); \\ Antti Karttunen, Sep 24 2017
(Scheme) (define (A267084 n) (if (zero? (modulo (A007504 n) n)) 0 1)) ;; Antti Karttunen, Sep 24 2017

Crossrefs

Cf. A007504, A045345 (positions of zeros), A060620, A158682, A225804.

Sequence in context: A011583 A011584 A011585 * A354807 A011586 A011587

Adjacent sequences: A267081 A267082 A267083 * A267085 A267086 A267087

Keyword

nonn,easy

Author

Ctibor O. Zizka, Jan 10 2016

Extensions

More terms and the second description added to the name by Antti Karttunen, Sep 24 2017

Status

approved