A180133 Smallest k such that k*6^n is a sum of two successive primes.

5, 2, 1, 1, 4, 12, 2, 1, 4, 3, 5, 8, 7, 34, 8, 11, 33, 26, 13, 9, 13, 90, 15, 40, 30, 5, 43, 9, 69, 38, 27, 79, 47, 9, 36, 6, 1, 92, 44, 51, 50, 16, 81, 21, 9, 50, 84, 14, 45, 59, 124, 215, 36, 6, 1, 20, 31, 35, 33, 46, 18, 3, 23, 114, 19, 41, 84, 14, 8, 35, 114, 19, 73, 14, 39, 68, 42

Offset

0,1

Comments

If a(n) == 0 (mod 6), then a(n+1) = a(n)/6.

Records: 5, 12, 34, 90, 92, 124, 215, 249, 592, 601, 1099, 1282, 1406, 1589, 1700, 2688, ..., .

Corresponding primes are twin primes for n = 0, 1, 2, 3, 4, 7, 13, 15, 28, 69, 120, 162, 251, 257, 279 ..., .

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..500

Mathematica

f[n_] := Block[{k = 1, j = 6^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 nextprime, prevprime
def sum2succ(n): return n == prevprime(n//2) + nextprime(n//2)
def a(n):
  if n == 0: return 5
  k, pow6 = 1, 6**n
  while not sum2succ(k*pow6): k += 1
  return k
print([a(n) for n in range(77)]) # Michael S. Branicky, May 02 2021

Crossrefs

Cf. A180130, A180131, A180132, A180134, A179975, A180135, A180136, A180137, A180138.

Sequence in context: A085119 A010128 A348993 * A197419 A029764 A136301

Adjacent sequences: A180130 A180131 A180132 * A180134 A180135 A180136

Keyword

nonn

Author

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

Status

approved