A091935 Smallest number of 1's in binary representations of primes between 2^n and 2^(n+1).

1, 2, 3, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 4, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3

Offset: 1

Author

Reinhard Zumkeller, Feb 14 2004

Keywords

• nonn

Comments

a(n) = A000120(A091936(n)).

0 never appears, 1 appears only at 1, 2's appear only for Fermat primes (A019434), 4's appear at A092100. I have found no fives <= 250. - Robert G. Wilson v

Links

• Robert Israel, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A091937, A092100.

Programs

Maple

f:= proc(n) local i,j,k;
  if isprime(2^n+1) then return 2 fi;
  for i from 1 to n-1 do if isprime(2^n+1+2^i) then return 3 fi od;
  for i from 1 to n-2 do for j from i+1 to n-1 do if isprime(2^n+2^i+2^j+1) then return 4 fi od od;
  error ">=5 found"
end proc:
f(1):= 1:
map(f, [$1..200]); # Robert Israel, Mar 30 2020

Mathematica

Run the second Mathematica line of A091936, then Join[{1}, Count[ IntegerDigits[ #, 2], 1] & /@ Table[ f[n], {n, 2, 105}]] (* Robert G. Wilson v, Feb 19 2004 *)

Extensions

More terms from Robert G. Wilson v, Feb 18 2004