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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
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
KEYWORD
nonn
AUTHOR
Jud McCranie, Nov 05 2001
EXTENSIONS
Offset changed from 0 to 1 by Harry J. Smith, Oct 04 2009
STATUS
approved