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A065044 Start of the first run of exactly n consecutive primes, none of which are twin primes. 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; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Viggo Brun proved that there exist arbitrarily long sequences of primes which are not twin primes (Ribenboim, page 261).
REFERENCES
Paulo Ribenboim, The New Book of Prime Number Records, Springer, 1996.
LINKS
David A. Corneth and Amiram Eldar, Table of n, a(n) for n = 1..342 (terms 1..100 from Harry J. Smith)
FORMULA
a(n) = A151800(A089637(n) + 2), for n > 1. - Amiram Eldar, Jan 15 2020
EXAMPLE
79 is the first prime in a run of four consecutive primes (79, 83, 89, 97), none of which are twin primes, and the next larger and smaller primes are each members of a twin pair, so a(4)=79.
PROG
(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)) ) } \\ Harry J. Smith, Oct 04 2009
CROSSREFS
Sequence in context: A118104 A107211 A069548 * A142313 A264776 A153213
KEYWORD
nonn
AUTHOR
Jud McCranie, Nov 05 2001
EXTENSIONS
Offset changed from 0 to 1 by Harry J. Smith, Oct 04 2009
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)