A180130 Smallest k such that k*2^n is a sum of two successive primes.

5, 4, 2, 1, 7, 4, 2, 1, 9, 15, 8, 4, 2, 1, 25, 19, 11, 12, 6, 3, 10, 5, 35, 33, 52, 26, 13, 28, 14, 7, 15, 38, 19, 45, 47, 26, 13, 43, 84, 42, 21, 39, 35, 18, 9, 46, 23, 43, 49, 104, 52, 26, 13, 48, 24, 12, 6, 3, 21, 36, 18, 9, 15, 15, 9, 42, 21, 23, 67, 62, 31, 64, 32, 16, 8, 4, 2, 1, 45

Offset: 0

Author

Zak Seidov & Robert G. Wilson v, Aug 15 2010

Keywords

• nonn

Comments

If a(n) == 0 (mod 2), then a(n+1) = a(n)/2.

Records: 5, 7, 9, 15, 25, 35, 52, 84, 104, 146, 284, 330, 645, 660, 1020, 1677, 1701, 1747, 2247, 2991, ..., .

Corresponding primes are twin primes for n = 0, 1, 2, 3, 8, 17, 18, 19, 23, 43, 44, 64, 156, 189, 190, 210, 211, 212, 264, 265, 281, 282, 283, 388, 547, 725, 726, 727, ..., .

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A180131, A180132, A180133, A180134, A179975, A180135, A180136, A180137, A180138.

Programs

Mathematica

f[n_] := Block[{k = 1, j = 2^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 79, 0]

Python

from sympy import isprime, nextprime, prevprime
def ok(n):
  if n <= 5: return n == 5
  return not isprime(n//2) and n == prevprime(n//2) + nextprime(n//2)
def a(n):
  k, pow2 = 1, 2**n
  while not ok(k*pow2): k += 1
  return k
print([a(n) for n in range(79)]) # Michael S. Branicky, May 04 2021