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

1,1

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.

References

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

Links

Table of n, a(n) for n=1..86.

Formula

sum(p(n)) mod 6.

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A007504, A103208.

Sequence in context: A299212 A249018 A235052 * A279404 A072970 A276320

Adjacent sequences: A102063 A102064 A102065 * A102067 A102068 A102069

Keyword

easy,nonn

Author

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

Extensions

More terms from Harvey P. Dale, Jun 19 2014

Status

approved