This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A218046 Primes p such that 8p + 2r is a primorial for some r in A006512. 2
 2, 11, 23, 83, 113, 131, 173, 191, 233, 239, 251, 263, 281, 293, 359, 419, 431, 449, 503, 641, 653, 659, 701, 719, 743, 761, 809, 821, 881, 911, 953, 1013, 1019, 1031, 1049, 1103, 1223, 1229, 1289, 1301, 1433, 1439, 1451, 1493, 1511, 1559, 1583, 1601, 1619 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The primes p in this sequence satisfy b#/2 = 4p + r,  where p is a prime, b# is a primorial, and r is the second of the twin prime pair (r-2, r). Each p is therefore associated with at least one primorial, and with a pair of twin primes. The empirical evidence suggests that each twin prime pair is associated with at least one p, and each p with a twin prime pair. I conjecture that this sequence (and therefore the sequence of twin primes) is infinite. LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..354 Michael Kaarhus, Twin Prime Conjectures 1, 2 and 3, 2012, (PDF) EXAMPLE 8*2   + 2*7 = 5# 8*11  + 2*61 = 7# 8*23  + 2*13 = 7# 8*83  + 2*823 = 11# 8*113 + 2*14563 = 13# 8*131 + 2*254731 = 17# 8*173 + 2*463 = 11# 8*191 + 2*14251 = 13# 8*233 + 2*14083 = 13# 8*239 + 2*199 = 11# 8*251 + 2*151 = 11# 8*263 + 2*103 = 11# 8*281 + 2*31 = 11# 8*293 + 2*307444891294244533 = 47# 8*359 + 2*253819 = 17# PROG (PARI) list(lim)={     my(v=List(), P=3, q);     forprime(p=5, lim,         P*=p;         forprime(t=2, min(lim, (P-2)\4),             q=P-4*t;             if(q%6==1 && ispseudoprime(q) && ispseudoprime(q-2), listput(v, t))         )     );     vecsort(Vec(v), , 8) }; \\ Charles R Greathouse IV, Oct 23 2012 CROSSREFS Sequence in context: A141423 A106974 A198277 * A217309 A115374 A078699 Adjacent sequences:  A218043 A218044 A218045 * A218047 A218048 A218049 KEYWORD nonn AUTHOR Michael G. Kaarhus, Oct 19 2012 EXTENSIONS Terms corrected by Charles R Greathouse IV, Oct 23 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 25 12:04 EDT 2019. Contains 322456 sequences. (Running on oeis4.)