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

0,1

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

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]

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, 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

Crossrefs

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

Sequence in context: A078981 A041555 A041747 * A192727 A056519 A295972

Adjacent sequences: A180131 A180132 A180133 * A180135 A180136 A180137

Keyword

nonn

Author

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

Status

approved