OFFSET
1,3
COMMENTS
Only 3d = 11b has an alternating sum of 0.
LINKS
Harry J. Smith, Table of n, a(n) for n=1..1000
William Paulsen, wpaulsen(AT)csm.astate.edu, Partitioning the [prime] maze
EXAMPLE
The sixth prime is 13d = 1101b -> -(1)+(1)-(0)+(1) = 1 = a(6)
MATHEMATICA
f[n_] := (d = Reverse[ IntegerDigits[n, 2]]; l = Length[d]; s = 0; k = 1; While[k < l + 1, s = s - (-1)^k*d[[k]]; k++ ]; s); Table[ Prime[ f[n]], {n, 1, 100} ]
PROG
(PARI)
baseE(x, b)=
{
local(d, e=0, f=1);
while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=10);
return(e)
}
SumAD(x)=
{
local(a=1, s=0);
while (x>9, s+=a*(x-10*(x\10)); x\=10; a=-a);
return(s + a*x)
}
{ for (n=1, 1000, p=prime(n);
s=SumAD(baseE(p, 2)); write("b065081.txt", n, " ", s) )
} \\ Harry J. Smith, Oct 06 2009
(PARI)
f(p)=
{
v=binary(p);
L=#v; u=1; s=0;
forstep(k=L, 1, -1, if(v[k]==1, s+=u); u=-u; );
return(s)
};
for(n=1, 100, p=prime(n); an=f(p); print1(an, ", ")) \\ Washington Bomfim, Jan 16 2011
(Python)
from sympy.ntheory import digits, prime
def A065081(n): return sum((0, 1, -1, 0)[i] for i in digits(prime(n), 4)[1:]) # Chai Wah Wu, Jul 19 2024
CROSSREFS
KEYWORD
base,easy,sign
AUTHOR
Robert G. Wilson v, Nov 09 2001
STATUS
approved