cp's OEIS Frontend

A139102 Numbers whose binary representation shows the distribution of prime numbers up to the n-th prime minus 1, using "0" for primes and "1" for nonprime numbers.

%I A139102 #25 Jan 10 2022 06:52:42
%S A139102 1,2,9,37,599,2397,38359,153437,2454999,157119967,628479869,
%T A139102 40222711647,643563386359,2574253545437,41188056726999,
%U A139102 2636035630527967,168706280353789919,674825121415159677,43188807770570219359,691020924329123509751,2764083697316494039005
%N A139102 Numbers whose binary representation shows the distribution of prime numbers up to the n-th prime minus 1, using "0" for primes and "1" for nonprime numbers.
%C A139102 a(n) is the decimal representation of A139101(n) interpreted as binary number.
%H A139102 Michael S. Branicky, <a href="/A139102/b139102.txt">Table of n, a(n) for n = 1..468</a>
%H A139102 Omar E. Pol, <a href="http://polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.
%F A139102 a(n) = A139104(n)/2.
%e A139102 a(4)=37 because 37 written in base 2 is 100101 and the string "100101" shows the distribution of prime numbers up to the 4th prime minus 1, using "0" for primes and "1" for nonprime numbers.
%p A139102 A139101 := proc(n) option remember ; local a,p; if n = 1 then RETURN(1); else a := 10*A139101(n-1) ; for p from ithprime(n-1)+1 to ithprime(n)-1 do a := 10*a+1 ; od: fi ; RETURN(a) ; end: # _R. J. Mathar_, Apr 25 2008
%p A139102 bin2dec := proc(n) local nshft ; nshft := convert(n,base,10) ; add(op(i,nshft)*2^(i-1),i=1..nops(nshft) ) ; end: # _R. J. Mathar_, Apr 25 2008
%p A139102 A139102 := proc(n) bin2dec(A139101(n)) ; end: # _R. J. Mathar_, Apr 25 2008
%p A139102 seq(A139102(n),n=1..35) ; # _R. J. Mathar_, Apr 25 2008
%t A139102 Table[ sum = 0; For[i = 1, i <= Prime[n] - 1 , i++, sum = sum*2;
%t A139102 If[! PrimeQ[i], sum++]]; sum, {n, 1, 25}] (* _Robert Price_, Apr 03 2019 *)
%o A139102 (PARI) a(n) = fromdigits(vector(prime(n)-1, k, !isprime(k)), 2); \\ _Michel Marcus_, Apr 04 2019
%o A139102 (Python)
%o A139102 from sympy import isprime, prime
%o A139102 def a(n):
%o A139102     return int("".join(str(1-isprime(i)) for i in range(1, prime(n))), 2)
%o A139102 print([a(n) for n in range(1, 22)]) # _Michael S. Branicky_, Jan 10 2022
%o A139102 (Python) # faster version for initial segment of sequence
%o A139102 from sympy import isprime
%o A139102 from itertools import count, islice
%o A139102 def agen(): # generator of terms
%o A139102     an = 0
%o A139102     for k in count(1):
%o A139102         an = 2 * an + int(not isprime(k))
%o A139102         if isprime(k+1):
%o A139102             yield an
%o A139102 print(list(islice(agen(), 21))) # _Michael S. Branicky_, Jan 10 2022
%Y A139102 Subset of A118255.
%Y A139102 Cf. A000040, A018252, A139101, A139103, A139104, A139119, A139120, A139122.
%K A139102 nonn,base
%O A139102 1,2
%A A139102 _Omar E. Pol_, Apr 08 2008
%E A139102 More terms from _R. J. Mathar_, Apr 25 2008
%E A139102 a(20)-a(21) from _Robert Price_, Apr 03 2019