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.
a(4) = 7 because the sum of the first 8 primes is 77 and 7 is its least prime divisor.
N:= 2000: # to use primes <= N P:= select(isprime, [2, seq(i, i=3..N, 2)]): A053790:= remove(isprime, ListTools:-PartialSums(P)): map(t -> min(numtheory:-factorset(t)), A053790); # Robert Israel, Jan 29 2018
Do[f=Sum[Prime[k],{k,1,2^n}]; If[PrimeQ[f],Print[{n,f}]],{n,0,32}]
a122516 n = a122516_list !! (n-1) a122516_list = filter ((== 1) . a010051) a046992_list -- Reinhard Zumkeller, Feb 25 2012
Flatten[Table[If[PrimeQ[Sum[ PrimePi[n], {n, 1, m}]], Sum[PrimePi[n], {n, 1, m}], {}], {m, 1, 200}]]
lst2={}; s2=0; Do[s2=s2+Prime[n]; If[PrimeQ[s2], AppendTo[lst2, s2]], {n, 4000000}]; lst3={}; s3=0; Do[s3=s3+lst2[[n]];If[PrimeQ[s3], AppendTo[lst3, s3]], {n,1,Length[lst2]}]; lst3; lst4={}; s4=0; Do[s4=s4+lst3[[n]];If[PrimeQ[s4], AppendTo[lst4, s4]], {n,1,Length[lst3]}]; lst4; lst5={}; s5=0; Do[s5=s5+lst4[[n]];If[PrimeQ[s5], AppendTo[lst5, s5]], {n,1,Length[lst4]}]; lst5
lst2={}; s2=0; Do[s2=s2+Prime[n]; If[PrimeQ[s2], AppendTo[lst2, s2]], {n, 10^9}]; lst3={}; s3=0; Do[s3=s3+lst2[[n]]; If[PrimeQ[s3], AppendTo[lst3, s3]], {n,1,Length[lst2]}]; lst3; lst4={}; s4=0; Do[s4=s4+lst3[[n]];If[PrimeQ[s4], AppendTo[lst4, s4]], {n,1,Length[lst3]}]; lst4; lst5={}; s5=0; Do[s5=s5+lst4[[n]];If[PrimeQ[s5], AppendTo[lst5, s5]], {n,1,Length[lst4]}]; lst5; lst6={}; s6=0; Do[s6=s6+lst5[[n]];If[PrimeQ[s6], AppendTo[lst6, s6]], {n,1,Length[lst5]}]; lst6
For n = 1, k(n) = 13 and a(n) = A007504(13) = 238 = 2*7*17. For n = 2, k(n) = 23 and a(n) = A007504(23) = 874 = 2*19*23. For n = 3, k(n) = 39 and a(n) = A007504(39) = 2914 = 2*31*47. For n = 4, k(n) = 41 and a(n) = A007504(41) = 3266 = 2*23*71. For n = 5, k(n) = 43 and a(n) = A007504(43) = 3638 = 2*17*107. For n = 6, k(n) = 47 and a(n) = A007504(47) = 4438 = 2*7*317. Note that for each of the elements of the sequence, omega(a(n)) = Omega(a(n)) = 3, i.e., the number of prime factors of a(n) = the number of distinct prime factors of a(n) = 3.
N:= 10^4: # to use primes up to N select(t -> numtheory:-bigomega(t)=3 and numtheory:-issqrfree(t), ListTools:-PartialSums(select(isprime,[2,seq(i,i=3..N,2)]))); # Robert Israel, Dec 15 2015
t = Accumulate@ Prime@ Range@ 300; Select[Range[2*10^5], And[MemberQ[t, #], PrimeNu@ # == PrimeOmega@ # == 3] &] (* Michael De Vlieger, Nov 27 2015, after Zak Seidov at A007504 *)
lista(nn) = {my(s = 0); for (n=1, nn, s += prime(n); if ((omega(s) == 3) && (bigomega(s)==3), print1(s, ", ")););} \\ Michel Marcus, Nov 28 2015
For n = 1, k(n) = 53 and a(n) = A007504(53) = 5830 = 2*5*11*53. For n = 2, k(n) = 57 and a(n) = A007504(57) = 6870 = 2*3*5*229. For n = 3, k(n) = 77 and a(n) = A007504(77) = 13490 = 2*5*19*71. For n = 4, k(n) = 84 and a(n) = A007504(84) = 16401 = 3*7*11*71. For n = 5, k(n) = 149 and a(n) = A007504(149) = 58406 = 2*19*29*53. For n = 6, k(n) = 151 and a(n) = A007504(151) = 60146 = 2*17*29*61. Note that for each of the elements of the sequence, omega(a(n)) = Omega(a(n)) = 4, i.e., the number of prime factors of a(n) = the number of distinct prime factors of a(n) = 4.
t = Accumulate@ Prime@ Range@ 600; Select[t, PrimeNu@ # == PrimeOmega@ # == 4 &] (* Michael De Vlieger, Nov 27 2015, after Zak Seidov at A007504 *)
lista(nn) = {my(s = 0); for (n=1, nn, s += prime(n); if ((omega(s) == 4) && (bigomega(s)==4), print1(s, ", ")););} \\ Michel Marcus, Nov 28 2015
5 = 2+3; 5 is a twin prime with 7. 17 = 2+3+5+7; 17 is a twin prime with 19. 41 = 2+3+5+7+11+13; 41 is a twin prime with 43. 197 = 2+3+5+7+11+13+17+19+23+29+31+37; 197 is a twin prime with 199.
Select[Accumulate @ Select[Range[45000], PrimeQ], PrimeQ[#] && PrimeQ[# + 2] &] (* Amiram Eldar, Aug 01 2021 *)
lista(nn) = {my(s=0); for (n=1, nn, s += prime(n); if (isprime(s) && isprime(s+2), print1(s, ", ")););} \\ Michel Marcus, Aug 21 2021
from itertools import accumulate from sympy import isprime, primerange list(filter(lambda p: isprime(p) and isprime(p+2), accumulate(primerange(2, 10000)))) # David Radcliffe, Aug 01 2021
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