|
|
A216684
|
|
Primes p such that p - phi(k)^2 is not prime for 1 <= phi(k)^2 < p.
|
|
0
|
|
|
2, 5, 13, 31, 37, 61, 127, 379, 439, 571, 619, 739, 829, 991, 1549, 3109, 3301, 3319, 5749, 7549, 7879, 48799
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
phi is the Euler totient function phi(n) : A000010.
A065377 is included in this sequence, and that one is probably finite.
|
|
LINKS
|
|
|
EXAMPLE
|
31 is in the sequence because :
31 - phi(1)^2 = 31 - 1^2 = 30 is composite;
31 - phi(2)^2 = 31 - 1^2 = 30 is composite;
31 - phi(3)^2 = 31 - 2^2 = 27 is composite;
31 - phi(4)^2 = 31 - 2^2 = 27 is composite;
31 - phi(5)^2 = 31 - 4^2 = 15 is composite;
31 - phi(6)^2 = 31 - 2^2 = 27 is the last composite because phi(7)^2 = 6^2 > 31.
|
|
MAPLE
|
with(numtheory):for n from 1 to 10000 do:ii:=0:p:=ithprime(n):for k from 1 to p while(p-phi(k)^2>0) do: if type(p- phi(k)^2, prime) =true then ii:=1:else fi:od:if ii=0 then printf(`%d, `, p):else fi:od:
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|