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

0,1

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

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]

Prog

(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

Crossrefs

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

Sequence in context: A232809 A011301 A316248 * A286593 A242376 A307393

Adjacent sequences: A180129 A180130 A180131 * A180133 A180134 A180135

Keyword

nonn

Author

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

Status

approved