A239708 Numbers of the form m = 2^i + 2^j, where i > j >= 0, such that m - 1 is prime.

3, 6, 12, 18, 20, 24, 48, 68, 72, 80, 132, 192, 258, 264, 272, 384, 1032, 1040, 1088, 1152, 1280, 2064, 2112, 4100, 4112, 4128, 4160, 5120, 6144, 8448, 16448, 20480, 32772, 32784, 32832, 33024, 33792, 65538, 65540, 65544, 65552, 65600, 66048, 73728, 81920, 262148, 262152, 262272, 262400, 263168, 266240, 294912, 524352, 528384, 786432

Offset: 1

Author

Hieronymus Fischer, Mar 27 2014

Keywords

• nonn

Comments

Complement of the disjunction of A079696 with A187813. This means that a number m is a term if and only if b = 2 is the only base for which the base-b digital sum of m is b.

Examples

			a(1) = 3, since 3 = 2^1 + 2^0.
a(3) = 12, since 12 = 2^3 + 2^2.
		

Links

• Hieronymus Fischer, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A239709 - A239720.

Cf. A239703, A187813, A079696, A008864.

Programs

Python

from itertools import islice
from sympy import isprime
def A239708_gen(): # generator of terms
    yield (n:=3)
    while True:
        n = n^((a:=-n&n+1)|(a>>1)) if n&1 else ((n&~(b:=n+(a:=n&-n)))>>a.bit_length())^b
        if isprime(n-1):
            yield n
A239708_list = list(islice(A239708_gen(),30)) # Chai Wah Wu, Mar 24 2025

Smalltalk

A239708
"Answers the n-th term of A239708.
  Usage: n A239708
  Answer: a(n)"
  | a b i k m p q terms |
  terms := OrderedCollection new.
  b := 2.
  p := 1.
  k := 0.
  m := 0.
  [k < self] whileTrue:
         [m := m + 1.
         p := b * p.
         q := 1.
         i := 0.
         [i < m and: [k < self]] whileTrue:
                   [i := i + 1.
                   a := p + q.
                   (a - 1) isPrime
                        ifTrue:
                            [k := k + 1.
                            terms add: a].
                   q := b * q]].
  ^terms at: self
-----------------

Smalltalk

A239708inv
  "Answers a kind of inverse of A239708.
  Usage: n A239708inv
  Answer: max ( k | A239708(k) < n)"
  | k |
  k := 1.
  [k A239708 < self] whileTrue: [k := k + 1].
  ^k - 1

Formula

A239703(a(n)) = 1.