A180136 Smallest k such that k*12^n is a sum of two successive primes.

5, 1, 1, 2, 18, 8, 13, 6, 2, 11, 11, 39, 20, 12, 1, 8, 9, 31, 182, 24, 2, 126, 128, 66, 9, 86, 146, 43, 170, 49, 155, 119, 115, 21, 77, 18, 60, 5, 119, 81, 27, 45, 81, 23, 28, 134, 14, 262, 131, 86, 55, 7, 549, 81, 199, 107, 100, 184, 85, 80, 32, 43, 118, 299, 43, 224, 187

Offset

0,1

Comments

If a(n) == 0 (mod 12), then a(n+1) = a(n)/12.

Records: 5, 18, 39, 182, 262, 549, 752, 811, 1456, ..., .

Corresponding primes are twin primes for n = 0, 1, 2, 5, 15, 26, 28, 55, 72, ..., .

Links

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

Mathematica

f[n_] := Block[{k = 1, j = 12^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 == 0: return 5
  k, pow12 = 1, 12**n
  while not sum2succ(k*pow12): k += 1
  return k
print([a(n) for n in range(67)]) # Michael S. Branicky, May 01 2021

Crossrefs

Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180135, A180137, A180138.

Sequence in context: A256503 A036791 A340513 * A346916 A359667 A010129

Adjacent sequences: A180133 A180134 A180135 * A180137 A180138 A180139

Keyword

nonn

Author

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

Status

approved