A112272 One seventh of the sum of the first n primes, when an integer.

4, 11, 34, 113, 284, 441, 634, 731, 943, 1226, 1657, 2343, 2469, 3767, 3931, 4271, 4712, 5759, 5963, 7154, 8221, 8467, 8971, 9362, 9763, 12655, 13279, 13595, 13915, 15941, 17560, 19641, 21261, 21675, 22091, 22937, 23363, 23793, 24671, 26702

Offset

1,1

Comments

a(1) = 4 and a(6) = 441 are perfect squares. What is the next term in this subsequence? Answer from Stefan Steinerberger: a(103)=315844=562^2.

References

Bach, E. and Shallit, J. Sect. 2.7 in Algorithmic Number Theory, Vol. 1: Efficient Algorithms. Cambridge, MA: MIT Press, 1996.

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Leo Moser, Notes on number theory. III. On the sum of consecutive primes, Canad. Math. Bull. 6 (1963), pp. 159-161.

Eric Weisstein's World of Mathematics, Prime Sums.

Formula

{a(n)} = {A007504(k)/7 iff 7 | A007504(k)}. {a(n)} = {(p_1 + p_2 + ... + p_k)/7 iff the sum is an integer}.

Example

a(1) = 4 = (2+3+5+7+11)/7 = A007504(5)/7 = 28/7.
a(2) = 11 = (2+3+5+7+11+13+17+19)/5 = A007504(8)/7 = 77/7.
a(3) = 34 = A007504(13)/5 = 238/7.
a(4) = 113 = A007504(22)/5 = 791/7.
a(5) = 284 = A007504(33)/5 = 1988/7.
a(6) = 441 = A007504(40)/5 = 3087/7.

Mathematica

s = 0; lst = {}; Do[s = s + Prime[n]; If[Mod[s, 7] == 0, AppendTo[lst, s/7]], {n, 270}]; lst (* Robert G. Wilson v *)
Select[Accumulate[Prime[Range[300]]]/7, IntegerQ] (* Harvey P. Dale, Nov 26 2014 *)

Crossrefs

Cf. A000040, A007504, A112040.

Sequence in context: A227329 A006765 A151272 * A149234 A149235 A149236

Adjacent sequences: A112269 A112270 A112271 * A112273 A112274 A112275

Keyword

easy,nonn

Author

Jonathan Vos Post, Nov 30 2005

Extensions

More terms from Stefan Steinerberger and Robert G. Wilson v, Dec 02 2005

Status

approved