A180135 Smallest k such that k*11^n is a sum of two successive primes.

5, 18, 6, 24, 6, 32, 40, 26, 20, 94, 50, 26, 10, 168, 30, 18, 196, 126, 70, 166, 30, 54, 130, 26, 50, 10, 40, 28, 20, 120, 84, 26, 228, 336, 92, 174, 24, 308, 28, 102, 216, 232, 68, 112, 192, 252, 512, 302, 110, 10, 330, 30, 138, 150, 168, 770, 70, 264, 24, 72, 180, 198

Offset: 0

Author

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

Keywords

• base
• nonn

Comments

If a(n) == 0 (mod 11), then a(n+1) = a(n)/11.

Records: 5, 18, 24, 32, 40, 94, 168, 196, 228, 336, 512, 770, 996, 1446, 1644, 1812, 1900, 3840, ..., .

Corresponding primes are twin primes for n = 0, 3, ..., .

Links

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

Crossrefs

Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180136, A180137, A180138.

Programs

Mathematica

f[n_] := Block[{k = 1, j = 11^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 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, pow11 = 1, 11**n
  while not ok(k*pow11): k += 1
  return k
print([a(n) for n in range(62)]) # Michael S. Branicky, May 18 2021