This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Table[ sum = 0; For[i = 1, i <= Prime[n] - 1 , i++, sum = sum*2;
If[! PrimeQ[i], sum++]]; IntegerString[sum, 2], {n, 1, 13}] (* Robert Price, Apr 03 2019 *)
a(n) = fromdigits(vector(prime(n)-1, k, !isprime(k)), 10); \\ Michel Marcus, Apr 04 2019
from sympy import isprime, prime
def a(n): return int("".join(str(1-isprime(i)) for i in range(1, prime(n))))
print([a(n) for n in range(1, 14)]) # Michael S. Branicky, Jan 10 2022
# 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 = 10 * an + int(not isprime(k))
if isprime(k+1):
yield an
print(list(islice(agen(), 13))) # Michael S. Branicky, Jan 10 2022
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.
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
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 *)
a(n) = fromdigits(vector(prime(n)-1, k, !isprime(k)), 2); \\ Michel Marcus, Apr 04 2019
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
# 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
Table[ sum = 0; For[i = 1, i <= Prime[n] , i++, sum = sum*2;
If[! PrimeQ[i], sum++]]; IntegerString[sum, 2], {n, 1, 20}] (* Robert Price, Apr 03 2019 *)
a(n) = fromdigits(vector(prime(n), k, !isprime(k)), 10); \\ Michel Marcus, Apr 04 2019
Select[Table[FromDigits[Boole /@ Not /@ PrimeQ /@ Range@k, 2], {k, 1, 100}], PrimeQ] (* Federico Provvedi, Oct 07 2013 *)
f(n) = fromdigits(vector(n, k, !isprime(k)), 2); \\ A118255 lista(nn) = for (n=1, nn, if (isprime(p=f(n)), print1(p, ", "))); \\ Michel Marcus, Apr 04 2019
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 *)
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, ", ")));
# uses agen() in A139102 from sympy import isprime print(list(islice(filter(isprime, agen()), 5))) # Michael S. Branicky, Jan 25 2022
a(7) = 119889 (in base 10) = 11101010001010001 (in base 2).
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123 5 7 1113 17
a[0] = 1; a[n_] := 2^(Prime[n] - 1) + Sum[2^(Prime[n] - Prime[k]), {k, 1, n}]; Table[a[n], {n, 0, 21}]
a(n) = if (n==0, 1, 2^(prime(n)-1) + sum(k=1, n, 2^(prime(n)-prime(k)))); \\ Michel Marcus, Mar 18 2020
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