A180131 Smallest k such that k*3^n is a sum of two successive primes.

5, 4, 2, 6, 2, 10, 20, 26, 22, 10, 16, 8, 8, 72, 24, 8, 18, 6, 2, 6, 2, 10, 20, 20, 22, 20, 52, 50, 104, 118, 84, 28, 38, 306, 102, 34, 100, 50, 30, 10, 192, 64, 46, 66, 22, 220, 84, 28, 176, 88, 30, 10, 8, 152, 292, 98, 82, 124, 160, 206, 106, 106, 160, 128, 78, 26, 110, 80

Offset

0,1

Comments

If a(n) == 0 (mod 3), then a(n+1) = a(n)/3.

Records: 5, 6, 10, 20, 26, 72, 104, 118, 306, 320, 348, 572, 824, 828, 972, 1054, 1110, 1540, ..., .

Corresponding primes are twin primes for n = 0, 1, 10, 13, 14, 15, 22, 102, ..., .

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..700

Mathematica

f[n_] := Block[{k = 1, j = 3^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 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, pow3 = 1, 3**n
  while not ok(k*pow3): k += 1
  return k
print([a(n) for n in range(68)]) # Michael S. Branicky, May 04 2021

Crossrefs

Cf. A180130, A180132, A180133, A180134, A179975, A180135, A180136, A180137, A180138.

Sequence in context: A094778 A260849 A246746 * A257972 A222307 A368274

Adjacent sequences: A180128 A180129 A180130 * A180132 A180133 A180134

Keyword

nonn

Author

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

Status

approved