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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. 9
1, 2, 9, 37, 599, 2397, 38359, 153437, 2454999, 157119967, 628479869, 40222711647, 643563386359, 2574253545437, 41188056726999, 2636035630527967, 168706280353789919, 674825121415159677, 43188807770570219359, 691020924329123509751, 2764083697316494039005 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the decimal representation of A139101(n) interpreted as binary number.

LINKS

Table of n, a(n) for n=1..21.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

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: # R. J. Mathar, Apr 25 2008

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

A139102 := proc(n) bin2dec(A139101(n)) ; end: # R. J. Mathar, Apr 25 2008

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 *)

PROG

(PARI) a(n) = fromdigits(vector(prime(n)-1, k, !isprime(k)), 2); \\ Michel Marcus, Apr 04 2019

CROSSREFS

Subset of A118255.

Cf. A000040, A018252, A139101, A139103, A139104, A139119, A139120, A139122.

Sequence in context: A218943 A122673 A241454 * A195187 A041515 A010750

Adjacent sequences:  A139099 A139100 A139101 * A139103 A139104 A139105

KEYWORD

nonn,base

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

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Last modified April 21 08:03 EDT 2021. Contains 343146 sequences. (Running on oeis4.)