A113617
Primes in the sums of the first 2^n primes or primes in A099825.
Original entry on oeis.org
2, 5, 17, 8893, 868151, 3875933, 219554912086470964379, 63036368490471985096643, 26151660747268050131008657684404431
Offset: 1
Sum of first 2^32 primes = 219554912086470964379 which is prime.
Offset corrected and a(8)-a(9) added by
Amiram Eldar, Jul 01 2024
A099824
a(n) = Sum of the first 10^n primes.
Original entry on oeis.org
2, 129, 24133, 3682913, 496165411, 62260698721, 7472966967499, 870530414842019, 99262851056183695, 11138479445180240497, 1234379338586942892505, 135436174616790289414111, 14738971133550183905879827, 1593061976858155930556059673, 171191473337951767580578821529
Offset: 0
For n=1, the sum of the first 10^1 = 10 primes is 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 129, so a(1) = 129. - _Michael B. Porter_, Aug 08 2016
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; k = p = 1; s = 0; Do[ While[p = NextPrim[p]; s = s + p; k < 10^n, k++ ]; k++; Print[s], {n, 0, 8}]
Table[Sum[Prime[i], {i, 10^n}], {n, 0, 5}] (* José de Jesús Camacho Medina, Dec 27 2014 *)
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vecA099824(n)={ my(s,c,k=1,L:list); L=List();
forprime(m=2,prime(10^n),s+=m;c++; if(c==k,listput(L,s);k*=10));
return(vector(#L,i,L[i]))} \\ R. J. Cano, Aug 12 2016
a(22) from
David Baugh using Kim Walisch's primesum program, Jun 21 2016
a(23) from
David Baugh using Kim Walisch's primesum program, Sep 26 2016
A099826
Sum of the first 3^n primes.
Original entry on oeis.org
2, 10, 100, 1264, 15116, 171148, 1864190, 19697700, 203534530, 2067129306, 20706364528, 205144046742, 2014349179358, 19632546354498, 190150622868298, 1831906588192414, 17567504017456404, 167794196312059488, 1597037992049539274
Offset: 0
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NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k]; k = p = 1; s = 0; Do[ While[p = NextPrim[p]; s = s + p; k < 10^n, k++ ]; k++; Print[s], {n, 0, 16}]
A113633
Sum of the first 5^n primes.
Original entry on oeis.org
2, 28, 1060, 39612, 1336090, 42157238, 1271530648, 37178373556, 1062895088910, 29878892909030, 828999068943506, 22762324818835316, 619715756464336328, 16753554900339748756, 450233110894196298638, 12038074430656287496566, 320451759639384414082274, 8497567719126134980044214
Offset: 0
The first 5^1 primes add up to 28.
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t = {}; c = 1; k = 3; s = 2; Do[ While[c < 5^n, If[PrimeQ[k], c++; s += k]; k += 2]; Print@s; AppendTo[t, s], {n, 0, 10}]; t (* Robert G. Wilson v, Jan 17 2006 *)
A113634
Sum of the first 6^n primes.
Original entry on oeis.org
2, 41, 2427, 132059, 6426919, 291627051, 12646104721, 531741567755, 21868328382007, 884528298065271, 35319715358896709, 1395934334687210019, 54710988941767714851, 2129404515458094306737, 82391816104703313499231, 3171892875586735205701385, 121577571158289668158700601
Offset: 0
The first 6^1 primes add up to 41.
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t = {}; c = 1; k = 3; s = 2; Do[While[c < 6^n, If[PrimeQ@k, c++; s += k]; k += 2]; Print@s; AppendTo[t, s], {n, 0, 9}]; t (* Robert G. Wilson v, Jan 17 2006 *)
A113635
Sum of the first 7^n primes.
Original entry on oeis.org
2, 58, 4888, 363288, 24047406, 1482656786, 87401659166, 4997438572618, 279544493456056, 15382405126365576, 835737977869494888, 44947274043643171988, 2397349106561086277820, 126986150948361831547964, 6687136917574958175921116, 350384258762032443770716600
Offset: 0
The first 7^1 primes add up to 58.
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t = {}; c = 1; k = 3; s = 2; Do[While[c < 7^n, If[ PrimeQ@k, c++; s += k]; k += 2]; Print@s; AppendTo[t, s], {n, 0, 9}]; t (* Robert G. Wilson v, Jan 17 2006 *)
Table[Total[Prime[Range[7^n]]],{n,0,7}] (* The program generates the first 8 terms of the sequence. *) (* Harvey P. Dale, Jan 18 2024 *)
A121248
Numbers k such that the sum of the first 2^k primes is a prime.
Original entry on oeis.org
0, 1, 2, 6, 9, 10, 32, 36, 55
Offset: 1
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Do[f=Sum[Prime[k],{k,1,2^n}]; If[PrimeQ[f],Print[{n,f}]],{n,0,32}]
A131590
Sum of the squares of the first 2^n primes.
Original entry on oeis.org
4, 13, 87, 1027, 13275, 155995, 1789395, 19523155, 204330315, 2081006083, 20605602003, 199966727443, 1908356153955, 17942429101363, 166591116531123, 1529578004981731, 13917470067182067, 125565110929591171, 1124685106917162579, 10009134886727192611
Offset: 0
The sum of the squares of the first 2^2 primes is a(2) = 4 + 9 + 25 + 49 = 87.
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Array[Total[Prime[Range[2^#]]^2]&,20,0] (* James C. McMahon, Feb 25 2025 *)
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sumprimesq(n,b) = { local(x,y,s,a); for(y=0,n, s=0; for(x=1,b^y, s+=prime(x)^2; ); print1(s","); ) }
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lista(pmax) = {my(s = 0, k = 0, pow = 1); forprime(p = 1, pmax, k++; s += p^2; if(k == pow, print1(s, ", "); pow *= 2));} \\ Amiram Eldar, Jul 06 2024
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from sympy import sieve, prime
def a(n): return sum(p*p for p in sieve.primerange(1, prime(2**n)+1))
print([a(n) for n in range(20)]) # Michael S. Branicky, Apr 13 2021
A104190
Sums of primes between successive powers of two.
Original entry on oeis.org
2, 8, 48, 270, 1392, 6862, 32440, 149114, 674344, 3003292, 13234674, 57809228, 250594424, 1079480960, 4624303560, 19720668918, 83744226026, 354354250476, 1494620712320, 6286217598392, 26370903868480, 110375582988186, 461002956906910, 1921809181446898, 7997638730622268
Offset: 0
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a = Table[Sum[Prime[i], {i, 2^n, 2^(n + 1) - 1}], {n, 0, 24}]
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