

A007468


Sum of next n primes.
(Formerly M1846)


16



2, 8, 31, 88, 199, 384, 659, 1056, 1601, 2310, 3185, 4364, 5693, 7360, 9287, 11494, 14189, 17258, 20517, 24526, 28967, 33736, 38917, 45230, 51797, 59180, 66831, 75582, 84463, 95290, 106255, 117424, 129945, 143334, 158167, 173828, 190013
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OFFSET

1,1


COMMENTS

If we arrange the prime numbers into a triangle, with 2 at the top, 3 and 5 in the second row, 7, 11 and 13 in the third row, and so on and so forth, this sequence gives the row sums.  Alonso del Arte, Nov 08 2011
In the first 20000 terms, the only perfect square > 1 is 207936 (n=38). Is it the only one? Is there some proof/conjecture?  Carlos Eduardo Olivieri, Mar 09 2015


REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = prime(1 + n(n1)/2) + ... + prime(n + n(n1)/2), where prime(i) is ith prime.


EXAMPLE

a(1)=2 because "sum of next 1 prime" is 2;
a(2)=8 because sum of next 2 primes is 3+5=8;
a(3)=31 because sum of next 3 primes is 7+11+13=31, etc.


MATHEMATICA

a[n_] := Sum[Prime[i], {i, 1+n(n1)/2, n+n(n1)/2}]; Table[a[n], {n, 100}]
With[{nn=40}, Total/@TakeList[Prime[Range[(nn(nn+1))/2]], Range[nn]]] (* Requires Mathematica version 11 or later *) (* Harvey P. Dale, Jan 15 2020 *)


CROSSREFS

Cf. A078721 and A011756 for the starting and ending prime of each sum.
Sequence in context: A266043 A265950 A294264 * A280156 A054137 A062456
Adjacent sequences: A007465 A007466 A007467 * A007469 A007470 A007471


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Simon Plouffe


EXTENSIONS

More terms from Zak Seidov, Sep 21 2002


STATUS

approved



