A180137 Smallest k such that k*13^n is a sum of two successive primes.

5, 4, 24, 4, 8, 22, 40, 4, 14, 16, 28, 10, 266, 40, 20, 46, 112, 156, 12, 20, 228, 26, 2, 220, 60, 140, 92, 42, 316, 132, 84, 70, 68, 50, 280, 164, 112, 146, 148, 30, 36, 126, 390, 30, 30, 38, 462, 114, 14, 86, 56, 168, 1600, 224, 104, 8, 72, 434, 142, 60, 750, 202, 318

Offset

0,1

Comments

If a(n) == 0 (mod 13), then a(n+1) = a(n)/13.

Records: 5, 24, 40, 266, 316, 390, 462, 1600, 2616, 5834, ..., .

Corresponding primes are twin primes for n = 0, 2, ..., .

Links

Robert G. Wilson v, Table of n, a(n) for n = 0..200

Mathematica

f[n_] := Block[{k = 1, j = 13^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, pow13 = 1, 13**n
  while not ok(k*pow13): k += 1
  return k
print([a(n) for n in range(63)]) # Michael S. Branicky, May 04 2021

Crossrefs

Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180135, A180136, A180138.

Sequence in context: A204930 A341102 A167636 * A288207 A038246 A176738

Adjacent sequences: A180134 A180135 A180136 * A180138 A180139 A180140

Keyword

nonn

Author

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

Status

approved