|
| |
|
|
A118584
|
|
Least n-digit prime in base 12 that is a twin prime and Sophie Germain prime of type 1.
|
|
0
|
|
|
|
3, 29, 179, 1931, 20771, 248867, 2986349, 35833079, 429983039, 5159780471, 61917366011, 743008372451, 8916100451231, 106993205386139, 1283918464561721, 15407021574604589, 184884258895077527
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
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".
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
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.
|
|
|
MAPLE
|
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;
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
easy,nonn,base
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
