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

1,1

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

Links

Table of n, a(n) for n=1..5.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A300926 A337306 A216539 * A123216 A307318 A058245

Adjacent sequences: A139119 A139120 A139121 * A139123 A139124 A139125

Keyword

nonn,base,more

Author

Omar E. Pol, Apr 11 2008

Extensions

a(5) from Robert Price, Apr 03 2019

Status

approved