A072225 Numbers n such that prime(n) + prime(n+1) + prime(n+2) is prime.

3, 4, 5, 7, 8, 9, 10, 11, 13, 16, 18, 19, 20, 22, 23, 26, 29, 34, 35, 37, 38, 45, 47, 50, 58, 60, 61, 62, 64, 68, 69, 70, 75, 77, 79, 80, 83, 87, 88, 90, 91, 94, 95, 97, 101, 113, 116, 119, 120, 121, 126, 128, 132, 133, 134

Offset

1,1

Comments

The sequence contains 298884 terms <= 2000000, so nearly 15% of the numbers <= 2000000 are in the sequence. - Dmitry Kamenetsky, Aug 08 2015

Heuristically, we might expect the "probability" of n being in the sequence to be on the order of 1/log(n). - Robert Israel, Aug 09 2015

The first 8 consecutive integers in this sequence start from 8744076. - Dmitry Kamenetsky, Aug 28 2015

The first 9 consecutive integers in this sequence start from 697642916. - Dmitry Kamenetsky, Sep 08 2015

Vladimir Chirkov found that the first 10 and 11 consecutive integers in this sequence start from 23169509240 and 29165083170, respectively (see The Prime Puzzles link). - Dmitry Kamenetsky, Sep 08 2015

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Carlos Rivera, Puzzle 798. A nice puzzle by Kamenetski, The Prime Puzzles & Problems Connection.

Example

9 is in the sequence because prime(9) + prime(10) + prime(11) = 23 + 29 + 31 = 83 is a prime.

Maple

a:=proc(n) if isprime(ithprime(n)+ithprime(n+1)+ithprime(n+2))=true then n else fi end: seq(a(n), n=1..150); # Emeric Deutsch, Apr 24 2006

Mathematica

Select[Range[10^4], PrimeQ[Prime[ # ] + Prime[ # + 1] + Prime[ # + 2]] &]

Prog

(Magma) [n: n in [0..600]| IsPrime(NthPrime(n)+NthPrime(n+1)+NthPrime(n+2))]; // Vincenzo Librandi, Apr 06 2011
(PARI) isok(n)=isprime(prime(n)+prime(n+1)+prime(n+2)) \\ Anders Hellström, Aug 20 2015

Crossrefs

Cf. A034962, A073681, A117673, A152469, A152470.

Sequence in context: A039131 A278637 A191979 * A137689 A081690 A081688

Adjacent sequences: A072222 A072223 A072224 * A072226 A072227 A072228

Keyword

easy,nonn

Author

Joseph L. Pe, Jul 04 2002

Status

approved