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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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Zak Seidov, A175783

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

Sequence in context: A298348 A303005 A320790 * A078722 A320791 A320792

Adjacent sequences:  A175780 A175781 A175782 * A175784 A175785 A175786

KEYWORD

nonn

AUTHOR

Zak Seidov, Sep 03 2010

STATUS

approved

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Last modified April 11 02:27 EDT 2021. Contains 342886 sequences. (Running on oeis4.)