A108325 "Binary prime squares": values of k for which k^2, expressed in base two and read as a decimal number, is a prime.

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

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 A159887 A159888 * 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