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A112272 One seventh of the sum of the first n primes, when an integer. 2
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 (list; graph; refs; listen; history; text; internal format)
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.

Moser, L. "Notes on Number Theory III. On the Sum of Consecutive Primes." Can. Math. Bull. 6, 159-161, 1963.

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

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

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Last modified August 14 13:16 EDT 2020. Contains 336480 sequences. (Running on oeis4.)