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.
is(m) = {my(s=0); if(isprime(m), for(i=1, m-1, if((s+=kronecker(i, m))<0, return(1)))); 0; }
a(n) = {my(c=0); forstep(m=2^n+3, 2^(n+1), 4, c+=is(m)); c; } \\ Jinyuan Wang, Jul 20 2020
isok(m) = {my(s=0); if(m%4==3, for(i=1, m-1, if((s+=kronecker(i, m))<0, return(1)))); 0; } \\ Jinyuan Wang, Jul 20 2020
def is_Motzkin(n, k):
s = 0
for i in (1..k) :
s += jacobi_symbol(i, n)
if s < 0 : return False
return True
def A095101_list(n):
return [m for m in range(3, n+1, 4) if not is_Motzkin(m, m//2)]
A095101_list(467) # Peter Luschny, Aug 08 2012
L = {}; Do[p = Prime[k]; If[Mod[p, 4] == 3 && Min[Table[Sum[JacobiSymbol[n, p], {n, 0, m}], {m, 0, p - 1}]] < 0, L = Append[L, p]], {k, 1, 192}]; L (* Jonathan Sondow, Oct 25 2011 *)
isok(m) = {my(s=0); if(m%4==3&&isprime(m), for(i=1, m-1, if((s+=kronecker(i, m))<0, return(1)))); 0; } \\ Jinyuan Wang, Jul 20 2020
def A095103_list(n) : def is_Motzkin(n, k): s = 0 for i in (1..k) : s += jacobi_symbol(i, n) if s < 0 : return false return true P = filter(is_prime, range(n+1)[3::4]) return filter(lambda m: not is_Motzkin(m, m//2), P) A095103_list(1163) # Peter Luschny, Aug 08 2012
13 is in the sequence because 13 is prime and 13 = 1101_2. '1101' has three 1's and one 0. 3 > 1 + 1. - _Indranil Ghosh_, Feb 07 2017
B(x) = {nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b1 > (b0+1), return(1);, return(0);); };
forprime(x = 3, 499, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 11 2011
from sympy import isprime
i = 1
j = 1
while j <= 2000:
bi = bin(i)[2:]
if isprime(i) and bi.count("1") > 1 + bi.count("0"):
print(str(j) + " " + str(i))
j += 1
i += 1 # Indranil Ghosh, Feb 07 2017
f:= proc(n) local L,d,s;
if not isprime(n) then return false fi;
L:= convert(n,base,2);
convert(L,`+`) > nops(L)/2+1
end proc:
select(f, [seq(i,i=3..1000,2)]); # Robert Israel, Oct 26 2023
n1Q[p_]:=Module[{be=IntegerDigits[p,2]},Total[be]>2+Count[be,0]]; Select[ Prime[ Range[150]],n1Q] (* Harvey P. Dale, Oct 26 2022 *)
B(x) = { nB = floor(log(x)/log(2)); b1 = 0; b0 = 0;
for(i = 0, nB, if(bittest(x,i), b1++;, b0++;); );
if(b1 > (2+b0), return(1);, return(0););};
forprime(x = 2, 859, if(B(x), print1(x, ", "); ); );
\\ Washington Bomfim, Jan 12 2011
Select[Flatten[Position[Mod[DigitCount[Select[Range[0, 5000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 1]] - 1, PrimeQ] (* Amiram Eldar, Feb 07 2023 *)
from sympy import fibonacci, primerange
def a(n):
k=0
x=0
while n>0:
k=0
while fibonacci(k)<=n: k+=1
x+=10**(k - 3)
n-=fibonacci(k - 1)
return x
def ok(n): return str(a(n)).count("1")%2
print([n for n in primerange(1, 1001) if ok(n)]) # Indranil Ghosh, Jun 08 2017
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