A108322 - OEIS

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.

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, 0, 0, 0, 0, 0, 0, 0, 0, 10111110001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 101000101001, 0, 101011111001, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1000110001001, 0, 0, 0, 0, 0, 0, 0, 0, 0

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OFFSET

1,29

COMMENTS

Another definition: numbers having only digits 1 and 0, which, read in base 10 are primes and in base 2 are perfect squares.

LINKS

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

EXAMPLE

a(5)=0 because 5^2 = 25 = 11001_2, and the decimal number 11001 is not prime.

a(29)=1101001001 because 29^2 = 841 = 1101001001_2, and the decimal number 1101001001 is prime.

MATHEMATICA

bps[n_]:=With[{c=FromDigits[IntegerDigits[n^2, 2]]}, If[PrimeQ[c], c, 0]]; Array[bps, 80] (* Harvey P. Dale, Jun 12 2024 *)