

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
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OFFSET

1,1


LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000


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

Cf. A108322, A108323, A108324.
Sequence in context: A166311 A159888 A159887 * A242555 A101007 A253252
Adjacent sequences: A108322 A108323 A108324 * A108326 A108327 A108328


KEYWORD

easy,nonn,base


AUTHOR

Alexandre Wajnberg, Jun 30 2005


EXTENSIONS

More terms from Emeric Deutsch, Jul 04 2005


STATUS

approved



