|
|
A267091
|
|
Primes p such that p*(2^k)+1 is also prime, where 2^k is the largest power of 2 smaller than p.
|
|
0
|
|
|
2, 3, 7, 11, 53, 59, 67, 73, 109, 149, 167, 239, 277, 307, 331, 421, 433, 457, 463, 487, 563, 593, 599, 683, 719, 743, 809, 821, 929, 971, 983, 1013, 1069, 1087, 1117, 1129, 1303, 1399, 1453, 1567, 1579, 1597, 1609, 1987, 2087, 2111, 2129, 2141, 2267, 2339, 2477
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The corresponding primes are 3, 7, 29, 89, 1697, 1889, 4289, 4673, 6977, 19073, 21377, 30593, 70913, 78593, 84737, 107777, 110849, 116993, 118529, 124673, 288257, 303617, 306689, 349697, 368129, 380417, 414209, 420353, 475649, 497153, 503297, ...
|
|
LINKS
|
|
|
EXAMPLE
|
3*(2^1)+1=7(is prime) => p=3, (2^k)=2; (2^k)<p; 2<3.
11*(2^3)+1=89(is prime) => p=11, (2^k)=8; (2^k)<p; 8<11.
73*(2^6)+1=4673(is prime) => p=73, (2^k)=64; (2^k)<p; 64<73.
|
|
MATHEMATICA
|
Select[Prime@ Range@ 400, PrimeQ[# 2^IntegerPart@ Log2@ # + 1] &] (* Michael De Vlieger, Jan 11 2016 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|