|
|
A226650
|
|
Numbers n such that the distance from 2^(2n) to the prev prime is the same as the distance from (2n)^2 to the prev prime.
|
|
0
|
|
|
1, 2, 5, 7, 10, 18, 52, 83, 113, 133, 169, 226, 347, 568, 909, 4612, 8014
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Numbers n such that 2^(2n) - (largest prime < 2^(2n)) = (2n)^2 -(largest prime < (2n)^2).
Primes in the sequence are: 2, 5, 7,...
|
|
LINKS
|
|
|
EXAMPLE
|
1 is in the sequence because the distance from 4 to 3 is the same as the distance from 4 to 3.
2 is in the sequence because the distance from 16 to 13 is the same as the distance from 16 to 13.
5 is in the sequence because the distance from 1024 to 1021 is the same as the distance from 100 to 97.
|
|
MATHEMATICA
|
dP[x_] := x - NextPrime[x, -1]; Select[Range[250]*2, (d = dP[#^2]; PrimeQ[2^# - d] && d == dP[2^#]) &]/2 (* Giovanni Resta, Jun 14 2013 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,less
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|