|
|
A175783
|
|
Primes p such that the sum of next p primes is prime.
|
|
1
|
|
|
3, 5, 11, 19, 37, 41, 113, 149, 163, 281, 421, 541, 547, 607, 661, 691, 739, 823, 827, 941, 991, 1013, 1019, 1093, 1249, 1453, 1549, 1553, 1583, 1619, 1733, 1747, 1951, 2069, 2153, 2239, 2399, 2549, 2609, 2663, 2687, 2741, 2777, 2803, 2833, 2857, 2861
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Primes p = prime(m) such that Sum_{k=1..p} prime(m+k) is prime. - Corrected by Zak Seidov, May 25 2017
|
|
LINKS
|
|
|
EXAMPLE
|
a(1) = 3 because sum s of 3 primes after 3, s = 5+7+11 = 23, is prime.
a(2) = 5 because sum s of 5 primes after 5, s = 7+11+13+17+19 = 67, is prime.
|
|
MATHEMATICA
|
Reap[Do[p = Prime[n]; If[PrimeQ[s = Sum[Prime[n + k], {k, p}]], Sow[p]], {n, 2, 1000}]][[2, 1]] (* corrected by Zak Seidov, May 25 2017 *)
|
|
PROG
|
(Magma) [p: i in [1..1000] | IsPrime(S) where S is &+[NthPrime(i+k): k in [1..p]] where p is NthPrime(i)]; // Bruno Berselli, May 25 2017
(PARI) list(lim)=my(v=List(), p=1, r=2, s=2, t); forprime(q=2, lim, s-=q; t=q-p+1; while(t, r=nextprime(r+1); s+=r; t--); if(isprime(s), listput(v, q)); p=q); Vec(v) \\ Charles R Greathouse IV, May 25 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|