

A109927


First primes p connected to two primes either by 2p+1 or 2p1 upward [downward (p1)/2 or (p+1)/2].


3



3, 5, 11, 23, 37, 83, 157, 179, 359, 661, 719, 877, 997, 1019, 1237, 1439, 1657, 2039, 2063, 2137, 2459, 2557, 2819, 2903, 2963, 3023, 3061, 3623, 3779, 3803, 3863, 4177, 4261, 4357, 4621, 4919, 5399, 5581, 5639, 6037, 6121, 6217, 6361, 6899, 6983, 7079
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OFFSET

1,1


COMMENTS

These primes may be part of Cunningham chains longer than three terms. It seems the two operators are never mixed, except for 3, 5 and 7: for 3, we have: 2 through <2p1> > 3 through <2p+1> > 7 for 5: 3 <2p1> > 5 <2p+1> > 11 for 7: 3 <2p+1> > 7 <2p1> > 13
For p > 7, such a mixed chain with p in the middle is impossible because the number 3 would be a nontrivial factor of either the smallest or the largest term.  Jeppe Stig Nielsen, May 05 2019
Primes (excluding 2 and 7) that divide more than one semiprime triangular number A068443.  Jeppe Stig Nielsen, May 05 2019
The disjoint union of A059455 and A109835.  Jeppe Stig Nielsen, May 05 2019


LINKS

Table of n, a(n) for n=1..46.
Chris Caldwell's Prime Glossary, Cunningham chains.


EXAMPLE

a(3)=11 is here because 5>11>23 through <2p+1>;
a(4)=23 because 11>23>47 through <2p+1>;
a(5)=37 because 19>37>73 through <2p1>.


PROG

Terms computed by Gilles Sadowski.
(PARI) forprime(p=3, 10^6, if(p%3==2, isprime((p1)/2)&&isprime(2*p+1), isprime((p+1)/2)&&isprime(2*p1))&&print1(p, ", ")) \\ Jeppe Stig Nielsen, May 05 2019


CROSSREFS

Cf. A005382, A005383, A005384, A005385, A059455, A068497.
Sequence in context: A117010 A056874 A280773 * A146276 A155753 A133914
Adjacent sequences: A109924 A109925 A109926 * A109928 A109929 A109930


KEYWORD

easy,nonn


AUTHOR

Alexandre Wajnberg, Aug 31 2005


STATUS

approved



