A102066 Sum of the first n primes, mod 6.

2, 5, 4, 5, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 3, 2, 3, 4, 3, 4, 5, 4, 3, 4, 3, 4, 3, 4, 3, 4, 3, 2, 3, 2, 3, 4, 5, 4, 3, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 4, 3, 4, 3, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 3, 4, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3

Offset: 1

Author

Alan Sutcliffe (alansut(AT)ntlworld.com), Dec 28 2004

Keywords

• easy
• nonn

Comments

Curiosity, it takes almost 60 terms before 1 and 0 appear. Stability arises from near equal (often alternating) occurrences of p mod 6 = 1 and p mod 6 = 5.

Examples

			a(5) = 4 since (2+3+5+7+11) mod 6 = 4.
		

References

• H. L. Nelson, "Prime Sums", J. Rec. Math., 14 (1981), 205-206.

Crossrefs

Cf. A007504, A103208.

Programs

Mathematica

Mod[Accumulate[Prime[Range[120]]],6] (* Harvey P. Dale, Jun 19 2014 *)

PARI

a(n) = sum(i=1, n, prime(i)) % 6 \\ Michel Marcus, Jul 12 2013

Formula

sum(p(n)) mod 6.

Extensions

More terms from Harvey P. Dale, Jun 19 2014