1,1

Let X be 10 and E be 11 in base 12. In base 12, all primes greater than 3 end in the digits 1,5,7,E. All twin primes (p,q) with p>3 end in the digits (5,7) or (E,1). All Sophie Germain primes of type 1 end in the digit 5 or E. A Cunningham chain of type 1 starts with a 5-prime or E-prime and all subsequent primes are E-primes. The sequence in base 12 is "3", "25", "12E", "114E", "1002E", "10002E", "1000265", "1000089E", "10000093E", "100000009E", "1000000104E", "10000000102E", "100000000187E", "1000000000410E", "100000000007535", "100000000000X665", "1000000000001E95E", "10000000000000E25E", "100000000000000099E", "1000000000000001447E", "10000000000000000544E", "100000000000000002797E", "1000000000000000000872E", "10000000000000000006806E".

29 is 25 in base 12 and is the first two digit prime that is twin (31=27 is its companion), and Sophie Germain of type 1, since 2*29+1=59=4E is prime.

istwin := proc(p::prime) isprime(p-2) or isprime(p+2) end: issophie := proc(p::prime) isprime(2*p+1) or isprime((p-1)/2) end: L:=[]: for w to 1 do for n from 1 to 24 do p:=nextprime(12^(n-1)); while not (istwin(p) and issophie(p)) do p:=nextprime(p) od; L:=[op(L), p]; od; od; L;

Cf. A001359, A006512, A005384, A118479.

Sequence in context: A096028 A137786 A112498 this_sequence A126185 A083092 A135163

Adjacent sequences: A118581 A118582 A118583 this_sequence A118585 A118586 A118587

easy,nonn

Walter Kehowski (wkehowski(AT)cox.net), May 17 2006