A092111 a(n) = n+1 minus the greatest number of 1's in the binary representations of primes between 2^n and 2^(n+1).

0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Robert G. Wilson v, Feb 20 2004

Keywords

• nonn

Comments

0's occur only at Mersenne prime exponents (A000043) - 1, twos are in A092112, threes do not appear < 504.

a(n) <= 2 for n <= 2000. - Robert Israel, Mar 05 2020

Links

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

Crossrefs

Cf. A091938, A092112.

Programs

Maple

f:= proc(n) local t,j,k;
  t:= 2^(n+1)-1;
  if isprime(t) then return 0 fi;
  for j from 1 to n-1 do if isprime(t-2^j) then return 1 fi od;
  for j from 1 to n-2 do for k from j+1 to n-1 do
    if isprime(t-2^j-2^k) then return 2 fi od od;
  FAIL
end proc:
map(f, [$1..200]); # Robert Israel, Mar 05 2020

Mathematica

Compute the second line of the Mathematica code for A091938, then (Table[n + 1, {n, 105}]) - (Count[ IntegerDigits[ #, 2], 1] & /@ Table[ f[n], {n, 105}])

Formula

a(n) = n+1 - A091937(n).