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URL: https://oeis.org/A139102

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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.
10
1, 2, 9, 37, 599, 2397, 38359, 153437, 2454999, 157119967, 628479869, 40222711647, 643563386359, 2574253545437, 41188056726999, 2636035630527967, 168706280353789919, 674825121415159677, 43188807770570219359, 691020924329123509751, 2764083697316494039005
OFFSET
1,2
COMMENTS
a(n) is the decimal representation of A139101(n) interpreted as binary number.
FORMULA
a(n) = A139104(n)/2.
EXAMPLE
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.
MAPLE
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:
bin2dec := proc(n) local nshft ; nshft := convert(n, base, 10) ; add(op(i, nshft)*2^(i-1), i=1..nops(nshft) ) ; end:
A139102 := proc(n) bin2dec(A139101(n)) ; end:
seq(A139102(n), n=1..35) ; # R. J. Mathar, Apr 25 2008
MATHEMATICA
Table[ sum = 0; For[i = 1, i <= Prime[n] - 1 , i++, sum = sum*2;
If[! PrimeQ[i], sum++]]; sum, {n, 1, 25}] (* Robert Price, Apr 03 2019 *)
With[{nn=100}, {bp=Table[If[PrimeQ[n], 0, 1], {n, nn}]}, Table[FromDigits[Take[bp, k], 2], {k, Prime[Range[PrimePi[nn]]]-1}]] (* Harvey P. Dale, Nov 24 2025 *)
PROG
(PARI) a(n) = fromdigits(vector(prime(n)-1, k, !isprime(k)), 2); \\ Michel Marcus, Apr 04 2019
(Python)
from sympy import isprime, prime
def a(n):
return int("".join(str(1-isprime(i)) for i in range(1, prime(n))), 2)
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Jan 10 2022
(Python) # faster version for initial segment of sequence
from sympy import isprime
from itertools import count, islice
def agen(): # generator of terms
an = 0
for k in count(1):
an = 2 * an + int(not isprime(k))
if isprime(k+1):
yield an
print(list(islice(agen(), 21))) # Michael S. Branicky, Jan 10 2022
CROSSREFS
KEYWORD
nonn,base,changed
AUTHOR
Omar E. Pol, Apr 08 2008
EXTENSIONS
More terms from R. J. Mathar, Apr 25 2008
a(20)-a(21) from Robert Price, Apr 03 2019
STATUS
approved