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A065706 Least member p1 of prime octuplets (p1, p2, p3, ..., p8 = p1 + 26), the eight p's being consecutive primes. 34
11, 17, 1277, 88793, 113147, 284723, 855713, 1146773, 2580647, 6560993, 15760091, 20737877, 25658441, 58208387, 69156533, 73373537, 74266253, 76170527, 93625991, 100658627, 134764997, 137943347, 165531257, 171958667 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
3 patterns for 8-tuplets: 11010011001011, 11011010011001 and v.v.
See A022011, A022012 and A022013 for the three different possible patterns. The sequence is conjectured to be infinite, although it is not even proved that there are infinitely many twin primes (p1, p2 = p1+2). - M. F. Hasler, May 02 2015
LINKS
Harry J. Smith and Dana Jacobsen, Table of n, a(n) for n = 1..18123 [first 100 terms from Harry J. Smith]
Tony Forbes and Norman Luhn, Prime k-tuplets
Norman Luhn, The smallest prime k-tuplets, database of compressed files.
Eric Weisstein's World of Mathematics, k-Tuple Conjecture
EXAMPLE
a(3) = 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303 = 1277+26 are primes.
PROG
(PARI) { n=0; p1=2; p8=19; for (m=1, 10^12, p1=nextprime(p1+1); p8=nextprime(p8+1); if (p8 - p1 == 26, write("b065706.txt", n++, " ", p1); if (n==100, return)) ) } \\ Harry J. Smith, Oct 26 2009
(Perl) use ntheory ":all"; my($s, $e, $i, %h)=(1, 1e10, 0); undef @h{sieve_prime_cluster($s, $e, 2, 6, 8, 12, 18, 20, 26), sieve_prime_cluster($s, $e, 2, 6, 12, 14, 20, 24, 26), sieve_prime_cluster($s, $e, 6, 8, 14, 18, 20, 24, 26)}; say ++$i, " $_" for sort {$a<=>$b} keys %h; # Dana Jacobsen, Oct 10 2015
CROSSREFS
11 = A065688(8), 26 = A008407(8), 8 = A023193(26+1), octets in A066082 are another (not minimal) constellation of 8 primes.
Union of A022011, A022012 and A022013.
See A257124 (prime septuplets) with an overview of prime k-tuplets.
Sequence in context: A226258 A056705 A259744 * A078874 A257169 A162555
KEYWORD
nonn
AUTHOR
Frank Ellermann, Dec 05 2001
STATUS
approved

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Last modified February 20 20:53 EST 2024. Contains 370217 sequences. (Running on oeis4.)