A092100 -id:A092100 - cp's OEIS frontend

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

Reinhard Zumkeller, Feb 14 2004

nonn

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

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

Cf. A091937, A092100.

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

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 *)

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

A092112 Where A092111 equals 2.

Original entry on oeis.org

14, 22, 26, 36, 38, 42, 54, 57, 62, 70, 78, 81, 90, 94, 110, 122, 132, 134, 138, 142, 147, 150, 158, 166, 168, 171, 172, 174, 178, 182, 190, 194, 198, 206, 210, 222, 238, 254, 285, 294, 312, 315, 318, 334, 336, 350, 366, 372, 382, 405, 414, 416, 432, 434, 446, 454

Offset: 1

Robert G. Wilson v, Feb 20 2004, corrected Nov 02 2006

nonn

Not as obvious as A092100, this sequence differs from multiples of 8 plus 6 (A017137).

Cf. A092111, A091935.

Run the second Mathematica line of A091938, then g[n_] := (n + 1 - Count[ IntegerDigits[f[n], 2], 1]); Select[ Range[100], g[ # ] == 2 &]

cp's OEIS Frontend

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

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