A348292 - OEIS

A348292

Binary expansion of the smallest binary number starting with a(0)=1 that is prime when the final number is 1 and composite when the final number is 0.

1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 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, 1, 0, 0, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 1

(list; constant; graph; refs; listen; history; text; internal format)

OFFSET

COMMENTS

The prime values generated by this sequence are also generated by A084435 (except for 2, which is only listed in A084435).

REFERENCES

Donald E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, problem 39, page 76.

LINKS

Table of n, a(n) for n=0..81.

EXAMPLE

For example, the binary numbers 1, 11, and 111 expressed in base 10 are 1, 3, and 7, which are prime with the exception of the first term. The next term in the binary number must be 0 because the binary number 1111 is composite.

MATHEMATICA

seq[len_] := Module[{s = {1}, k = 1, m = 1, d}, While[k < len, m *= 2; d = Boole@PrimeQ[m + 1]; m += d; AppendTo[s, d]; k++]; s]; seq[100] (* Amiram Eldar, Oct 19 2021 *)

PROG

(HTML/JavaScript)

<html>

binary="1";

for(k=0; k<30; k++)

{

if(isprime(parseInt(binary+"1", 2))==true)

{

binary=binary+"1";

}

if(isprime(parseInt(binary+"1", 2))==false)

{

binary=binary+"0";

}

document.write(binary);

function isprime(x)

{

for(i=2; i<(x-1); i++)

{

if(x%i==0)

{

return false;

}

return true;

}

</script>

</html>

CROSSREFS

Cf. A084435.

Sequence in context: A374048 A090174 A165556 * A127243 A127248 A266298

Adjacent sequences: A348289 A348290 A348291 * A348293 A348294 A348295

KEYWORD

nonn,base,cons

AUTHOR

Michael R. Page, Oct 19 2021

STATUS

approved