A139122 Primes whose binary representation shows the distribution of prime numbers up to some prime minus 1, using "0" for primes and "1" for nonprime numbers.

2, 37, 599, 153437, 628479869

Offset: 1

Author

Omar E. Pol, Apr 11 2008

Keywords

• nonn
• base
• more

Comments

Primes in A139102.

a(6) > 10^14632 if it exists (no further primes in first 5000 terms of A139102). - Michael S. Branicky, Jan 25 2022

Crossrefs

Cf. A118255, A118256, A118257, A139101, A139102, A139103, A139104, A139119, A139120.

Programs

Mathematica

Select[Table[ sum = 0; For[i = 1, i <= Prime[n] - 1 , i++, sum = sum*2; If[! PrimeQ[i], sum++]]; sum, {n, 1, 1000}], PrimeQ[#] &] (* Robert Price, Apr 03 2019 *)
Module[{nn=500,p,x},p=Table[If[PrimeQ[n],0,1],{n,nn}];x=SequencePosition[p,{1,0}][[All,1]];Join[{2},Select[Table[FromDigits[Take[p,k],2],{k,x}],PrimeQ]]] (* Harvey P. Dale, Jun 15 2022 *)

PARI

f(n) = fromdigits(vector(prime(n)-1, k, !isprime(k)), 2); \\ A139102
lista(nn) = for (n=1, nn, if (isprime(p=f(n)), print1(p, ", ")));

Python

# uses agen() in A139102
from sympy import isprime
print(list(islice(filter(isprime, agen()), 5))) # Michael S. Branicky, Jan 25 2022

Extensions

a(5) from Robert Price, Apr 03 2019