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URL: https://oeis.org/A072225

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A072225
Numbers k such that prime(k) + prime(k+1) + prime(k+2) is prime.
10
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 and A386275). - Dmitry Kamenetsky, Sep 08 2015
LINKS
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. A386275 (first occurrences of runs).
Sequence in context: A039131 A278637 A191979 * A137689 A081690 A081688
KEYWORD
easy,nonn
AUTHOR
Joseph L. Pe, Jul 04 2002
STATUS
approved