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A180136 Smallest k such that k*12^n is a sum of two successive primes. 9
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 (list; graph; refs; listen; history; text; internal format)
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 A010129 A073050

Adjacent sequences:  A180133 A180134 A180135 * A180137 A180138 A180139

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 1 22:23 EDT 2022. Contains 354984 sequences. (Running on oeis4.)