A089228 - OEIS

%I #22 Aug 10 2023 03:33:28

%S 1,3,5,7,9,13,19,25,29,31,49,51,57,97,99,103,109,119,123,127,163,169,

%T 179,185,195,207,209,211,213,217,221,223,233,235,239,251,261,269,273,

%U 289,295,297,303,325,329,333,347,369,371,375,409,439,449,453,455,467

%N Numbers m such that 1 + Sum_{k=1..m} prime(k) is prime.

%C Also numbers n such that the sum of the first n "primes", as defined in A008578, is prime. Analogous to A013916. - _Robert G. Wilson v_, May 19 2015

%C Integers k such that A007504(k) + 1 is prime. - _Michel Marcus_, Aug 10 2023

%H Robert Israel, <a href="/A089228/b089228.txt">Table of n, a(n) for n = 1..10000</a>

%e 25 is a term: 1 + Sum_{k=1..25} prime(k) = 1061 is prime.

%p a:=proc(n) if isprime(1+add(ithprime(k),k=1..n))=true then n else fi end: seq(a(n),n=1..600); # _Emeric Deutsch_, Jul 02 2005

%p # alternative

%p Primes:= select(isprime,[2,seq(2*i+1,i=1..10^5)]):

%p PS:= ListTools:-PartialSums(Primes):

%p select(t -> isprime(PS[t]+1), [$1..nops(PS)]); # _Robert Israel_, May 19 2015

%t Position[1 + Accumulate@ Prime@ Range@ 600, _?(PrimeQ@# &)] // Flatten (* after Harvey P. Dale from A013916 *) (* _Robert G. Wilson v_, May 19 2015 *)

%o (PARI) for(n=1,10^3,if(isprime(1+sum(i=1,n,prime(i))),print1(n,", "))) \\ _Derek Orr_, May 19 2015

%Y Cf. A007504, A008578, A013916, A014284.

%K nonn

%O 1,2

%A _Yalcin Aktar_, Dec 10 2003

%E Corrected and extended by _Emeric Deutsch_, Jul 02 2005