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%I A108322 #20 Jun 12 2024 15:40:20
%S A108322 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1101001001,0,
%T A108322 0,0,0,0,0,0,0,0,10111110001,0,0,0,0,0,0,0,0,0,0,0,101000101001,0,
%U A108322 101011111001,0,0,0,0,0,0,0,0,0,0,0,0,0,1000110001001,0,0,0,0,0,0,0,0,0
%N A108322 "Binary prime squares": a(n) = n^2 written in base 2 and interpreted as a base-10 number, if that number is prime; a(n) = 0 otherwise.
%C A108322 Another definition: numbers having only digits 1 and 0, which, read in base 10 are primes and in base 2 are perfect squares.
%H A108322 Harvey P. Dale, <a href="/A108322/b108322.txt">Table of n, a(n) for n = 1..1000</a>
%e A108322 a(5)=0 because 5^2 = 25 = 11001_2, and the decimal number 11001 is not prime.
%e A108322 a(29)=1101001001 because 29^2 = 841 = 1101001001_2, and the decimal number 1101001001 is prime.
%t A108322 bps[n_]:=With[{c=FromDigits[IntegerDigits[n^2,2]]},If[PrimeQ[c],c,0]]; Array[bps,80] (* _Harvey P. Dale_, Jun 12 2024 *)
%Y A108322 Cf. A108323, A108324, A108325.
%K A108322 easy,nonn,base
%O A108322 1,29
%A A108322 _Alexandre Wajnberg_, Jun 30 2005
%E A108322 Edited by _Jon E. Schoenfield_, Sep 23 2018
%E A108322 Offset corrected by _Michel Marcus_, Sep 24 2018

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