|
|
A108325
|
|
"Binary prime squares": values of k for which k^2, expressed in base two and read as a decimal number, is a prime.
|
|
4
|
|
|
29, 39, 51, 53, 67, 85, 87, 107, 135, 181, 189, 235, 253, 297, 351, 375, 379, 445, 449, 493, 583, 599, 613, 701, 715, 725, 739, 749, 769, 781, 831, 841, 847, 853, 921, 953, 1007, 1093, 1273, 1339, 1443, 1511, 1543, 1569, 1575, 1587, 1619, 1681, 1697, 1705
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
EXAMPLE
|
a(3)=51 because 51^2 = 2601 is the third perfect square whose binary representation 101000101001 read as the decimal one 101000101001 is prime.
|
|
MAPLE
|
a:=proc(n) if isprime(convert(n^2, binary))=true then n else fi end: seq(a(n), n=1..2400); # Emeric Deutsch, Jul 04 2005
|
|
MATHEMATICA
|
Select[Range[1800], PrimeQ[FromDigits[IntegerDigits[#^2, 2]]]&] (* Harvey P. Dale, May 23 2021 *)
|
|
PROG
|
(PARI) isok(n) = isprime(fromdigits(binary(n^2))); \\ Michel Marcus, Sep 24 2018
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|