A180132 Smallest k such that k*5^n is a sum of two successive primes.

5, 1, 4, 10, 2, 8, 12, 12, 36, 12, 28, 66, 30, 6, 18, 132, 36, 108, 34, 14, 48, 60, 12, 22, 150, 30, 6, 74, 54, 16, 8, 66, 150, 30, 6, 14, 374, 110, 22, 82, 62, 66, 108, 348, 114, 428, 190, 38, 570, 114, 102, 24, 82, 86, 178, 420, 84, 108, 328, 186, 126, 192, 76, 82, 24

Offset: 0

Author

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

Keywords

• nonn

Comments

If a(n) == 0 (mod 5), then a(n+1) = a(n)/5.

Records: 5, 10, 12, 36, 66, 132, 150, 374, 428, 570, 734, 840, 1938, 2036, 2220, 2968, 3132, 3444, 4014, 6090, ..., .

Corresponding primes are twin primes for n = 0, 1, 51, 102, 103, 202, 275, ..., .

Links

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

Crossrefs

Cf. A180130, A180131, A180133, A180134, A179975, A180135, A180136, A180137, A180138.

Programs

Mathematica

f[n_] := Block[{k = 1, j = 5^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 nextprime, prevprime
def sum2succ(n): return n == prevprime(n//2) + nextprime(n//2)
def a(n):
  if n < 2: return [5, 1][n]
  k, pow5 = 1, 5**n
  while not sum2succ(k*pow5): k += 1
  return k
print([a(n) for n in range(65)]) # Michael S. Branicky, May 01 2021