This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
lista(nn) = {s = 0; forprime(p=2, nn, s += p; if (isprime(s) && isprime(s-2), print1(p, ", ")););} \\ Michel Marcus, Feb 23 2015
2 is a term because 2 is prime and equals Sum_{2}. This is the trivial case.
281 is a term because 281 is prime and equals Sum_{2,3,...,41,43}, also Sum_{2,3,...,41,43,47,...,277,281} = 7699 which is also prime.
listp(nn) = {my(s=0); forprime(p=2, nn, s += p; if (isprime(s), my(ss = 0); forprime(q=2, s, ss += q); if (isprime(ss), print1(s, ", "));););} \\ Michel Marcus, Apr 11 2019
ListTools:-PartialSums(select(isprime, [seq(i,i=3..1000,2)])); # Robert Israel, Feb 12 2017
Accumulate@ Prime@ Range[2, 49] (* Michael De Vlieger, Feb 12 2017 *)
a(n) = sum(k=1, n+1, prime(k)) - 2; \\ Michel Marcus, Feb 12 2017
a013918 n = a013918_list !! (n-1) a013918_list = filter ((== 1) . a010051) a007504_list -- Reinhard Zumkeller, Feb 09 2015
Select[Accumulate[Prime[Range[1000]]], PrimeQ] (* Vladimir Joseph Stephan Orlovsky, Sep 01 2008 *)
n=0;forprime(k=2,2300,n=n+k;if(isprime(n),print(n))) \\ Michael B. Porter, Jan 29 2010
from sympy import isprime, nextprime; m = p = 0
while p < 2280:
p = nextprime(p); m += p
if isprime(m): print(m, end = ', ') # Ya-Ping Lu, Dec 24 2024
6 is a term because the sum of the first six primes 2 + 3 + 5 + 7 + 11 + 13 = 41 is prime.
P:=Filtered([1..5300],IsPrime);; a:=Filtered([1..Length(P)],n->IsPrime(Sum([1..n],k->P[k])));; Print(a); # Muniru A Asiru, Jan 04 2019
p=primes(10000); m=1;
for u=1:700 ; suma=sum(p(1:u));
if isprime(suma)==1 ; sol(m)=u; m=m+1; end
end
sol; % Marius A. Burtea, Jan 04 2019
[n:n in [1..700] | IsPrime(&+PrimesUpTo(NthPrime(n))) ]; // Marius A. Burtea, Jan 04 2019
p:=proc(n) if isprime(sum(ithprime(k),k=1..n))=true then n else fi end: seq(p(n),n=1..690); # Emeric Deutsch
s = 0; Do[s = s + Prime[n]; If[PrimeQ[s], Print[n]], {n, 1, 1000}]
Flatten[Position[Accumulate[Prime[Range[2000]]], ?(PrimeQ[#] &)]] (* _Harvey P. Dale, Dec 16 2010 *)
Flatten[Position[PrimeQ[Accumulate[Prime[Range[2000]]]],True]] (* Fred Patrick Doty, Aug 15 2017 *)
isA013916(n) = isprime(sum(i=1,n,prime(i))) \\ Michael B. Porter, Jan 29 2010
from sympy import isprime, prime
def aupto(lim):
s = 0
for k in range(1, lim+1):
s += prime(k)
if isprime(s): print(k, end=", ")
aupto(680) # Michael S. Branicky, Feb 28 2021
Primes:= select(isprime, [seq(2*i+1,i=1..10^4)]): L:= ListTools:-PartialSums(Primes): select(i -> isprime(L[i]), [$1..nops(L)]); # Robert Israel, May 19 2015
Position[Accumulate@ Prime@ Range[2, 750], ?(PrimeQ@# &)] // Flatten (* _Robert G. Wilson v, May 19 2015, after Harvey P. Dale in A013916 *)
s=n=0; forprime(p=3,1e4, n++; if(isprime(s+=p), print1(n", "))) \\ Charles R Greathouse IV, May 13 2015
29 is a prime and 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 = 127 (also a prime), so 29 is a term. - _Jon E. Schoenfield_, Mar 29 2021
SoddP := proc(n)
option remember;
if n <= 2 then
0;
elif isprime(n) then
procname(n-1)+n;
else
procname(n-1);
fi ;
end proc:
isA071150 := proc(n)
if isprime(n) and isprime(SoddP(n)) then
true;
else
false;
end if;
end proc:
n := 1 ;
for i from 3 by 2 do
if isA071150(i) then
printf("%d %d\n",n,i) ;
n := n+1 ;
end if;
end do: # R. J. Mathar, Feb 13 2015
Function[s, Select[Array[Take[s, #] &, Length@ s], PrimeQ@ Total@ # &][[All, -1]]]@ Prime@ Range[2, 640] (* Michael De Vlieger, Jul 18 2017 *) Module[{nn=650,pr},pr=Prime[Range[2,nn]];Table[If[PrimeQ[Total[Take[ pr, n]]], pr[[n]],Nothing],{n,nn-1}]] (* Harvey P. Dale, May 12 2018 *)
from sympy import isprime, nextprime
def aupto(limit):
p, s, alst = 3, 3, []
while p <= limit:
if isprime(s): alst.append(p)
p = nextprime(p)
s += p
return alst
print(aupto(4789)) # Michael S. Branicky, Mar 29 2021
PrimePi /@ Select[ FoldList[Plus, 0, Prime@ Range@450], PrimeQ@# &] (* Robert G. Wilson v Sep 28 2006 *) PrimePi/@Select[Accumulate[Prime[Range[500]]],PrimeQ] (* Harvey P. Dale, Jun 05 2013 *)
5 is in the sequence for the sum of all primes <= 5 is 10, and 10 has no prime divisor > 5. 17 is not in the sequence for the corresponding sum is 58 which has a prime divisor > 17.
p = s = 2; lst = {}; While[p < 1000, If[ FactorInteger[s][[-1, 1]] <= p, AppendTo[lst, p]]; p = NextPrime@ p; s = s + p]; lst (* Robert G. Wilson v, Feb 09 2017 *)
isok(n) = isprime(n) && (vecmax(factor(sum(k=1, primepi(n), prime(k)))[,1]) <= n); \\ Michel Marcus, Feb 12 2017
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