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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.
3
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
Javier Cilleruelo and Florian Luca, On the sum of the first n primes, Q. J. Math. 59:4 (2008), 14 pp.
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
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