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.
In the range ]2^4,2^5] 17 (10001 in binary) is the only such prime thus a(2) = 1.
In the range ]2^2,2^3] 5 (101 in binary) is the only such prime thus a(1) = 1. Similarly, in the range ]2^4,2^5] 19 (10011 in binary) is also unique in that respect, thus a(2) = 1 as well.
F:= combinat[fibonacci]:
b:= proc(n) option remember; local j;
if n=0 then 0
else for j from 2 while F(j+1)<=n do od;
b(n-F(j))+2^(j-2)
fi
end:
a:= proc(n) option remember; local p;
p:= `if`(n=1, 1, a(n-1));
do p:= nextprime(p);
if b(p)::even then break fi
od; p
end:
seq(a(n), n=1..100); # Alois P. Heinz, Mar 27 2016
F = Fibonacci;
b[n_] := b[n] = Module[{j},
If[n == 0, 0, For[j = 2, F[j + 1] <= n, j++];
b[n - F[j]] + 2^(j - 2)]];
a[n_] := a[n] = Module[{p},
p = If[n == 1, 1, a[n - 1]]; While[True,
p = NextPrime[p]; If[ EvenQ[b[p]], Break[]]]; p];
Array[a, 100] (* Jean-François Alcover, Jul 01 2021, after Alois P. Heinz *)
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))[-1]=="0"
print([n for n in primerange(1, 1001) if ok(n)]) # Indranil Ghosh, Jun 07 2017
r = Map[Fibonacci, Range[2, 12]]; Select[Prime@ Range@ 144, Last@ Flatten@ Map[Position[r, #] &, Abs@ Differences@ NestWhileList[Function[k, k - SelectFirst[Reverse@ r, # < k &]], # + 1, # > 1 &]] == 1 &] (* Michael De Vlieger, Mar 27 2016, Version 10 *)
genit(maxx)={for(n=1,maxx,q=(n-1)+(n+sqrtint(5*n^2))\2; if(isprime(q), print1(q,",")));} \\ Bill McEachen, Mar 26 2016
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))[-1]=="1"
print([n for n in primerange(1, 1001) if ok(n)]) # Indranil Ghosh, Jun 07 2017
is(m) = {if(!isprime(m), return(0)); my(s=0); for(i=1, m-1, if((s+=kronecker(i, m))<0, return(0))); 1; }
a(n) = {my(c=0); forstep(m=2^n+3*(n>1), 2^(n+1), 4, c+=is(m)); c; } \\ Jinyuan Wang, Jul 20 2020