A180134 Smallest k such that k*7^n is a sum of two successive primes.

5, 6, 18, 10, 30, 18, 4, 28, 4, 30, 30, 60, 120, 38, 12, 6, 52, 120, 70, 10, 102, 60, 70, 10, 186, 174, 42, 6, 90, 146, 154, 22, 18, 140, 20, 168, 24, 240, 60, 80, 26, 286, 154, 22, 12, 196, 28, 4, 2, 128, 116, 156, 422, 130, 204, 84, 12, 118, 88, 240, 536, 564, 798, 114

Offset: 0

Author

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

Keywords

• nonn

Comments

If a(n) == 0 (mod 7), then a(n+1) = a(n)/7.

Records: 5, 6, 18, 30, 60, 120, 186, 240, 286, 422, 536, 564, 798, 1010, 1074, 1334, 1434, 1474, 3706, 4108, 4370, 6160, ..., .

Corresponding prime are twin primes for n = 0, 17, 369, ..., .

Links

• Robert G. Wilson v, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A180130, A180131, A180132, A180133, A179975, A180135, A180136, A180137, A180138.

Programs

Mathematica

f[n_] := Block[{k = 1, j = 7^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, pow7 = 1, 7**n
  while not ok(k*pow7): k += 1
  return k
print([a(n) for n in range(64)]) # Michael S. Branicky, May 06 2021