A152535 -id:A152535 - cp's OEIS frontend

A007504 Sum of the first n primes.

0, 2, 5, 10, 17, 28, 41, 58, 77, 100, 129, 160, 197, 238, 281, 328, 381, 440, 501, 568, 639, 712, 791, 874, 963, 1060, 1161, 1264, 1371, 1480, 1593, 1720, 1851, 1988, 2127, 2276, 2427, 2584, 2747, 2914, 3087, 3266, 3447, 3638, 3831, 4028, 4227, 4438, 4661, 4888

Offset: 0

N. J. A. Sloane, Robert G. Wilson v

It appears that a(n)^2 - a(n-1)^2 = A034960(n). - Gary Detlefs, Dec 20 2011
This is true. Proof: By definition we have A034960(n) = Sum_{k = (a(n-1)+1)..a(n)} (2*k-1). Since Sum_{k = 1..n} (2*k-1) = n^2, it follows A034960(n) = a(n)^2 - a(n-1)^2, for n > 1. - Hieronymus Fischer, Sep 27 2012 [formulas above adjusted to changed offset of A034960 - Hieronymus Fischer, Oct 14 2012]
Row sums of the triangle in A037126. - Reinhard Zumkeller, Oct 01 2012
Ramanujan noticed the apparent identity between the prime parts partition numbers A000607 and the expansion of Sum_{k >= 0} x^a(k)/((1-x)...(1-x^k)), cf. A046676. See A192541 for the difference between the two. - M. F. Hasler, Mar 05 2014
For n > 0: row 1 in A254858. - Reinhard Zumkeller, Feb 08 2015
a(n) is the smallest number that can be partitioned into n distinct primes. - Alonso del Arte, May 30 2017
For a(n) < m < a(n+1), n > 0, at least one m is a perfect square.
Proof: For n = 1, 2, ..., 6, the proposition is clear. For n > 6, a(n) < ((prime(n) - 1)/2)^2, set (k - 1)^2 <= a(n) < k^2 < ((prime(n) + 1)/2)^2, then k^2 < (k - 1)^2 + prime(n) <= a(n) + prime(n) = a(n+1), so m = k^2 is this perfect square. - Jinyuan Wang, Oct 04 2018
For n >= 5 we have a(n) < ((prime(n)+1)/2)^2. This can be shown by noting that ((prime(n)+1)/2)^2 - ((prime(n-1)+1)/2)^2 - prime(n) = (prime(n)+prime(n-1))*(prime(n)-prime(n-1)-2)/4 >= 0. - Jianing Song, Nov 13 2022
Washington gives an oscillation formula for |a(n) - pi(n^2)|, see links. - Charles R Greathouse IV, Dec 07 2022

E. Bach and J. Shallit, §2.7 in Algorithmic Number Theory, Vol. 1: Efficient Algorithms, MIT Press, Cambridge, MA, 1996.
H. L. Nelson, "Prime Sums", J. Rec. Math., 14 (1981), 205-206.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. J. Mathar, Table of n, a(n) for n = 0..100000
C. Axler, On a Sequence involving Prime Numbers, J. Int. Seq. 18 (2015) # 15.7.6.
Christian Axler, New bounds for the sum of the first n prime numbers, arXiv:1606.06874 [math.NT], 2016.
P. Hecht, Post-Quantum Cryptography: S_381 Cyclic Subgroup of High Order, International Journal of Advanced Engineering Research and Science (IJAERS, 2017) Vol. 4, Issue 6, 78-86.
R. J. Mathar, Table of 100000n, a(100000n) for n = 1..10000
Romeo Meštrović, Curious conjectures on the distribution of primes among the sums of the first 2n primes, arXiv:1804.04198 [math.NT], 2018.
Vladimir Shevelev, Asymptotics of sum of the first n primes with a remainder term
Nilotpal Kanti Sinha, On the asymptotic expansion of the sum of the first n primes, arXiv:1011.1667 [math.NT], 2010-2015.
Lawrence C. Washington, Sums of Powers of Primes II, arXiv preprint (2022). arXiv:2209.12845 [math.NT]
Eric Weisstein's World of Mathematics, Prime Sums
OEIS Wiki, Sums of powers of primes divisibility sequences

Cf. A000041, A034386, A111287, A013916, A013918 (primes), A045345, A050247, A050248, A068873, A073619, A034387, A014148, A014150, A178138, A254784, A254858.
See A122989 for the value of Sum_{n >= 1} 1/a(n).
Cf. A008472, A002110, A038107.

P:=Filtered([1..250],IsPrime);;
a:=Concatenation([0],List([1..Length(P)],i->Sum([1..i],k->P[k]))); # Muniru A Asiru, Oct 07 2018

a007504 n = a007504_list !! n
a007504_list = scanl (+) 0 a000040_list
-- Reinhard Zumkeller, Oct 01 2014, Oct 03 2011

[0] cat [&+[ NthPrime(k): k in [1..n]]: n in [1..50]]; // Bruno Berselli, Apr 11 2011 (adapted by Vincenzo Librandi, Nov 27 2015 after Hasler's change on Mar 05 2014)

s1:=[2]; for n from 2 to 1000 do s1:=[op(s1),s1[n-1]+ithprime(n)]; od: s1;
A007504 := proc(n)
    add(ithprime(i), i=1..n) ;
end proc: # R. J. Mathar, Sep 20 2015

Accumulate[Prime[Range[100]]] (* Zak Seidov, Apr 10 2011 *)
primeRunSum = 0; Table[primeRunSum = primeRunSum + Prime[k], {k, 100}] (* Zak Seidov, Apr 16 2011 *)

A007504(n) = sum(k=1,n,prime(k)) \\ Michael B. Porter, Feb 26 2010

a(n) = vecsum(primes(n)); \\ Michel Marcus, Feb 06 2021

from itertools import accumulate, count, islice
from sympy import prime
def A007504_gen(): return accumulate(prime(n) if n > 0 else 0 for n in count(0))
A007504_list = list(islice(A007504_gen(),20)) # Chai Wah Wu, Feb 23 2022

a(n) ~ n^2 * log(n) / 2. - Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 24 2001 (see Bach & Shallit 1996)
a(n) = A014284(n+1) - 1. - Jaroslav Krizek, Aug 19 2009
a(n+1) - a(n) = A000040(n+1). - Jaroslav Krizek, Aug 19 2009
a(A051838(n)) = A002110(A051838(n)) / A116536(n). - Reinhard Zumkeller, Oct 03 2011
a(n) = min(A068873(n), A073619(n)) for n > 1. - Jonathan Sondow, Jul 10 2012
a(n) = A033286(n) - A152535(n). - Omar E. Pol, Aug 09 2012
For n >= 3, a(n) >= (n-1)^2 * (log(n-1) - 1/2)/2 and a(n) <= n*(n+1)*(log(n) + log(log(n))+ 1)/2. Thus a(n) = n^2 * log(n) / 2 + O(n^2*log(log(n))). It is more precise than in Fares's comment. - Vladimir Shevelev, Aug 01 2013
a(n) = (n^2/2)*(log n + log log n - 3/2 + (log log n - 3)/log n + (2 (log log n)^2 - 14 log log n + 27)/(4 log^2 n) + O((log log n/log n)^3)) [Sinha]. - Charles R Greathouse IV, Jun 11 2015
G.f: (x*b(x))/(1-x), where b(x) is the g.f. of A000040. - Mario C. Enriquez, Dec 10 2016
a(n) = A008472(A002110(n)), for n > 0. - Michel Marcus, Jul 16 2020

More terms from Stefan Steinerberger, Apr 11 2006

a(0) = 0 prepended by M. F. Hasler, Mar 05 2014

A206817 Sum_{0

Original entry on oeis.org

1, 10, 73, 520, 3967, 33334, 309661, 3166468, 35416555, 430546642, 5655609529, 79856902816, 1206424711303, 19419937594990, 331860183278677, 6000534640290364, 114462875817046051, 2297294297649673738, 48394006967070653425

Offset: 2

Clark Kimberling, Feb 12 2012

nonn

In the following guide to related sequences,

c(n) = Sum_{0

t(n) = Sum_{0

s(k).................c(n)........t(n)

k....................A000217.....A000292

k^2..................A016061.....A004320

k^3..................A206808.....A206809

k^4..................A206810.....A206811

k!...................A206816.....A206817

prime(k).............A152535.....A062020

prime(k+1)...........A185382.....A206803

2^(k-1)..............A000337.....A045618

k(k+1)/2.............A007290.....A034827

k-th quarter-square..A049774.....A206806

			a(3) = (2-1) + (6-1) + (6-2) = 10.

Danny Rorabaugh, Table of n, a(n) for n = 2..400

Cf. A000142, A206816.

s[k_] := k!; t[1] = 0;
p[n_] := Sum[s[k], {k, 1, n}];
c[n_] := n*s[n] - p[n];
t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1];
Table[c[n], {n, 2, 32}]          (* A206816 *)
Flatten[Table[t[n], {n, 2, 20}]] (* A206817 *)

a(n)=sum(j=1,n,j!*(2*j-n-1)) \\ Charles R Greathouse IV, Oct 11 2015

a(n)=my(t=1); sum(j=1,n,t*=j; t*(2*j-n-1)) \\ Charles R Greathouse IV, Oct 11 2015

[sum([sum([factorial(k)-factorial(j) for j in range(1,k)]) for k in range(2,n+1)]) for n in range(2,21)] # Danny Rorabaugh, Apr 18 2015

a(n) = a(n-1)+(n-1)s(n)-p(n-1), where s(n) = n! and p(k) = 1!+2!+...+k!.

a(n) = Sum_{k=2..n} A206816(k).

A185382 Sum_{j=1..n-1} P(n)-P(j), where P(j) = A065091(j) is the j-th odd prime.

Original entry on oeis.org

0, 2, 6, 18, 26, 46, 58, 86, 134, 152, 212, 256, 280, 332, 416, 506, 538, 640, 712, 750, 870, 954, 1086, 1270, 1366, 1416, 1520, 1574, 1686, 2092, 2212, 2398, 2462, 2792, 2860, 3070, 3286, 3434, 3662, 3896, 3976, 4386, 4470, 4642, 4730, 5270

Offset: 1

Clark Kimberling, Feb 13 2012

nonn

It appears 1/3 of a(n) values are divisible by 3 (as measured up to n = 8000). Almost all of these cases occur consecutively (i.e., in "runs"). The sizes of these runs, including runs of 1, in the first 250 primes are given by this sequence: {2, 4, 1, 1, 2, 4, 2, 2, 3, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 5, 6, 3, 2, 2, 3, 3, 9, 1, ..} with two runs up to 12 in length occurring in the first 5000 primes. - Richard R. Forberg, Mar 26 2015

a(n+1) == a(n) (mod 3) iff n == 0 (mod 3) or P(n+1) == P(n) (mod 3); this should have asymptotic probability 2/3, and explains some of the above comment. - Robert Israel, Mar 26 2015

			a(4)=(11-3)+(11-5)+(11-7)=18.

Robert Israel, Table of n, a(n) for n = 1..10000 (corrected by Ray Chandler, Jan 19 2019)

Cf. A001223, A152535, A206802 (a(n)/2), A206803 (= partial sums of this), A206804, A206817.

N:= 1000: # to get terms for all odd primes <= N
P:= select(isprime,[seq(2*i+1, i=1..floor((N-1)/2))]):
Q:= ListTools[PartialSums](P):
seq(n*P[n]-Q[n],n=2..nops(P)); # Robert Israel, Mar 26 2015

s[k_] := Prime[k + 1]; p[n_] := Sum[s[k], {k, 1, n}]; c[n_] := n*s[n] - p[n]; Table[c[n], {n, 2, 100}]

A185382(n)=(n-1)*prime(n+1)-sum(k=2,n-1,prime(k)) \\ M. F. Hasler, May 02 2015

a(n) = (n-1)*A065091(n) - A071148(n-1) = (n-1)*prime(n+1) - sum_{1 < k <= n} prime(k). [Corrected and extended by M. F. Hasler, May 02 2015]
a(n) = A206803(n) - A206803(n-1).
a(n) = Sum_{j=1..n-1} j*A001223(j+1). - Robert Israel, Mar 26 2015

Edited and a(1)=0 prefixed by M. F. Hasler, May 02 2015

A230850 A054541 and A000012 interleaved.

Original entry on oeis.org

2, 1, 1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 6, 1, 2, 1, 6, 1, 4, 1, 2, 1, 4, 1, 6, 1, 6, 1, 2, 1, 6, 1, 4, 1, 2, 1, 6, 1, 4, 1, 6, 1, 8, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 14, 1, 4, 1, 6, 1, 2, 1, 10, 1, 2, 1, 6, 1, 6, 1, 4, 1, 6, 1, 6, 1, 2, 1, 10, 1, 2, 1

Offset: 1

Omar E. Pol, Oct 31 2013

nonn

a(n) is also the length of the n-th edge of a staircase which represents the function pi(x) on the first quadrant of the square grid, see A000720.
a(2n-1) is the length of the n-th horizontal edge in the staircase.
a(2n) is the length of the n-th vertical edge in the staircase.
For another version see A230849.

			Illustration of initial terms, n = 1..22:
.
1                                                              _ _|
1                                                  _ _ _ _ _ _|
1                                          _ _ _ _|
1                                      _ _|
1                              _ _ _ _|
1                          _ _|
1                  _ _ _ _|
1              _ _|
1          _ _|
1        _|
1    _ _|
.
.      2 1   2   2       4   2       4   2       4           6   2
.
Drawing vertical line segments below the staircase (as shown below) we have that the number of cells in the vertical bars gives 0 together A000720.
Drawing horizontal line segments above the staircase we have that the number of cells in the k-th horizontal bar is A000040(k).
.    _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
31  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
29  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | |
23  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | |
19  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | |
17  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | |
13  |_ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | |
11  |_ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | | | |
7   |_ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | | | | | | | |
5   |_ _ _ _ _| | | | | | | | | | | | | | | | | | | | | | | | | | |
3   |_ _ _| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
2   |_ _|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|
.
.    0 0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10
.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Cf. A000012, A000040, A000720, A001223, A007504, A046992, A054541, A141042, A152535, A182986, A230849.

Riffle[Join[{2},Differences[Prime[Range[100]]]],1] (* Paolo Xausa, Oct 31 2023 *)

A230850(n) = if(1==n,2,if((n%2),prime((n+1)/2)-prime(((n+1)/2)-1),1)); \\ Antti Karttunen, Dec 23 2018

a(1) = 2; for n > 1, a(n) = A230849(n). - Antti Karttunen, Dec 23 2018

A090942 n-th arithmetic mean = prime(n).

Original entry on oeis.org

2, 4, 9, 13, 27, 23, 41, 33, 55, 83, 51, 103, 89, 69, 103, 143, 155, 95, 175, 147, 113, 205, 171, 227, 289, 201, 155, 215, 165, 229, 547, 255, 329, 205, 489, 221, 373, 385, 319, 407, 419, 263, 611, 279, 373, 289, 763, 787, 419, 327, 433, 545, 345, 781, 581, 593

Offset: 1

Amarnath Murthy, Dec 29 2003

nonn

Partial sums give A033286. - Omar E. Pol, Apr 20 2015

In other words, this is the unique sequence such that for all n >= 1, (1/n) * Sum_{k=1..n} a(k) = prime(n). - Antti Karttunen, Apr 30 2015

			From _Omar E. Pol_, Apr 20 2015: (Start)
Illustration of initial terms:
Consider a diagram in the first quadrant of the square grid in which the length of the n-th horizontal line segment is equal to the n-th prime, as shown below:
.   _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
.  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  51|
.  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _          83|   |
.  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _      55|           |   |
.  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _  33|       |           |   |
.  |_ _ _ _ _ _ _ _ _ _ _ _ _      41|   |       |           |   |
.  |_ _ _ _ _ _ _ _ _ _ _  23|       |   |       |           |   |
.  |_ _ _ _ _ _ _      27|   |       |   |       |           |   |
.  |_ _ _ _ _  13|       |   |       |   |       |           |   |
.  |_ _ _   9|   |       |   |       |   |       |           |   |
.  |_ _ 4|   |   |       |   |       |   |       |           |   |
.  |_2_|_|_ _|_ _|_ _ _ _|_ _|_ _ _ _|_ _|_ _ _ _|_ _ _ _ _ _|_ _|
.
a(n) is also the area (or the number of cells) in the n-th region of the diagram. For example: a(4) = 7 + 6 = 13.
(End)

G. C. Greubel, Table of n, a(n) for n = 1..10000

Cf. A000040, A007504, A033286, A033287, A141042, A152535.

[n le 1 select 2 else n*NthPrime(n) - (n-1)*NthPrime(n-1): n in [1..60]]; // G. C. Greubel, Feb 04 2019

Table[If[n==1, 2, nPrime@n -(n-1)Prime[n-1]], {n, 60}] (* Michael De Vlieger, Apr 20 2015 *)

vector(60, n, if(n==1,2, n*prime(n) -(n-1)*prime(n-1))) \\ G. C. Greubel, Feb 04 2019

[2] + [n*nth_prime(n) - (n-1)*nth_prime(n-1) for n in (2..60)] # G. C. Greubel, Feb 04 2019

a(n) = n*prime(n) - (n-1)*prime(n-1).
a(n) = A033287(n-2), n>1. - R. J. Mathar, Sep 08 2008
a(n) = A000040(n) + A141042(n-1), n >=2. - Omar E. Pol, Apr 20 2015

Corrected and extended by Ray Chandler, Dec 31 2003

A230849 A075526 and A000012 interleaved.

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 6, 1, 2, 1, 6, 1, 4, 1, 2, 1, 4, 1, 6, 1, 6, 1, 2, 1, 6, 1, 4, 1, 2, 1, 6, 1, 4, 1, 6, 1, 8, 1, 4, 1, 2, 1, 4, 1, 2, 1, 4, 1, 14, 1, 4, 1, 6, 1, 2, 1, 10, 1, 2, 1, 6, 1, 6, 1, 4, 1, 6, 1, 6, 1, 2, 1, 10, 1, 2, 1

Offset: 1

Omar E. Pol, Nov 01 2013

nonn

a(n) is also the length of the n-th edge of a staircase which represents the function pi(x) on the first quadrant of the square grid, see A000720.
a(2n-1) is the length of the n-th horizontal edge in the staircase.
a(2n) is the length of the n-th vertical edge in the staircase.
For another version see A230850.

			Illustration of initial terms, n = 1..22:
.
1                                                            _ _|
1                                                _ _ _ _ _ _|
1                                        _ _ _ _|
1                                    _ _|
1                            _ _ _ _|
1                        _ _|
1                _ _ _ _|
1            _ _|
1        _ _|
1      _|
1    _|
.
.    1 1   2   2       4   2       4   2       4           6   2
.
Drawing vertical line segments below the staircase (as shown below) we have that the number of cells in the vertical bars gives A000720.
Drawing horizontal line segments above the staircase we have that the number of cells in the k-th horizontal bar is A006093(k).
.    _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
30  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _|
28  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | |
22  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | |
18  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | |
16  |_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | |
12  |_ _ _ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | |
10  |_ _ _ _ _ _ _ _ _ _| | | | | | | | | | | | | | | | | | | | |
6   |_ _ _ _ _ _| | | | | | | | | | | | | | | | | | | | | | | | |
4   |_ _ _ _| | | | | | | | | | | | | | | | | | | | | | | | | | |
2   |_ _| | | | | | | | | | | | | | | | | | | | | | | | | | | | |
1   |_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|_|
.
.    0 1 2 2 3 3 4 4 4 4 5 5 6 6 6 6 7 7 8 8 8 8 9 9 9 9 9 9 10 10
.

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A000012, A000040, A000720, A001223, A006093, A007504, A046992, A075526, A141042, A152535, A230850.

Riffle[Join[{1},Differences[Prime[Range[100]]]],1] (* Paolo Xausa, Oct 31 2023 *)

A230849(n) = if((n%2)&&(n>1),prime((n+1)/2)-prime(((n+1)/2)-1),1); \\ Antti Karttunen, Dec 23 2018

A189892 a(n) = n*prime(n) - sum_{i=1..n-1} prime(i).

Original entry on oeis.org

2, 4, 10, 18, 38, 50, 78, 94, 130, 190, 212, 284, 336, 364, 424, 520, 622, 658, 772, 852, 894, 1026, 1118, 1262, 1462, 1566, 1620, 1732, 1790, 1910, 2344, 2472, 2670, 2738, 3088, 3160, 3382, 3610, 3766, 4006, 4252, 4336, 4766, 4854, 5034, 5126, 5690

Offset: 1

Bruno Berselli, Apr 30 2011

			a(4) = 4*prime(4) - (prime(3) + prime(2) + prime(1)) = 4*7 - (5 + 3 + 2) = 18.

Bruno Berselli, Table of n, a(n) for n = 1..5000

Cf. A152535, A166448.

[2] cat [n*NthPrime(n)-(&+[NthPrime(k): k in [1..n-1]]): n in [2..47]];

nn=50;Join[{2},With[{prs=Accumulate[Prime[Range[nn]]]},Table[n*Prime[n]-prs[[n-1]],{n,2,nn}]]] (* Harvey P. Dale, Nov 21 2014 *)

v=vector(10000);s=n=i=0;forprime(p=2,1e9,v[i++]=n++*p-s;if(i==#v,return,s+=p)) \\ Charles R Greathouse IV, May 01 2011

a(n) = A033286(n+1) - A007504(n) for n>1.

Showing 1-10 of 11 results. Next

cp's OEIS Frontend

A152563 Primes in A152535.

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A007504 Sum of the first n primes.

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A033286 a(n) = n * prime(n).

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A141042 Product of n and the n-th gap between primes: a(n) = n*A001223(n).

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A206817 Sum_{0

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A185382 Sum_{j=1..n-1} P(n)-P(j), where P(j) = A065091(j) is the j-th odd prime.

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