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

0,1

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

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]

Prog

(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

Crossrefs

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

Sequence in context: A349409 A109430 A085917 * A242600 A102593 A090462

Adjacent sequences: A180127 A180128 A180129 * A180131 A180132 A180133

Keyword

nonn

Author

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

Status

approved