|
Search: id:A065044
|
|
|
| A065044 |
|
Start of the first occurrence of exactly n primes such that none of them are twin primes. |
|
+0
1
|
|
| 2, 47, 113, 79, 2273, 1097, 467, 1327, 1163, 353, 5749, 3011, 5297, 10151, 1493, 9467, 887, 673, 13033, 9049, 15373, 8641, 28759, 83737, 13411, 18553, 14633, 44777, 54037, 60271, 59693, 142169, 77719, 61583, 178939, 26267, 122887, 293269
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
V. Brun proved that there exist arbitrarily long sequences of primes which are not twin primes( Ribenboim, page 261).
|
|
REFERENCES
|
P. Ribenboim, The New Book of Prime Number Records, Springer, 1996.
|
|
LINKS
|
Harry J. Smith, Table of n, a(n) for n=1,...,100
|
|
EXAMPLE
|
79 is the first prime in a sequence of four consecutive primes (79, 83, 89, 97), none of which are twin primes, the next larger and smaller primes are members of a twin pair, so a(4)=79.
|
|
PROGRAM
|
(PARI) nextTwin(t)= { until (isprime(t + 2), t=nextprime(t + 3)); return(t) } { default(primelimit, 4294965247); for (n=1, 100, u=2; until((primepi(u) - primepi(t) - 2) == n, t=u; u=nextTwin(t)); if (n==1, t=-3); write("b065044.txt", n, " ", nextprime(t + 3)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 04 2009]
|
|
CROSSREFS
|
Cf. A001097, A001359.
Sequence in context: A118104 A107211 A069548 this_sequence A142313 A153213 A128822
Adjacent sequences: A065041 A065042 A065043 this_sequence A065045 A065046 A065047
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Jud McCranie (j.mccranie(AT)comcast.net), Nov 05 2001
|
|
EXTENSIONS
|
OFFSET changed from 0,1 to 1,1 by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 04 2009
|
|
|
Search completed in 0.002 seconds
|
