A180137 - OEIS

%I #11 May 06 2021 21:21:08

%S 5,4,24,4,8,22,40,4,14,16,28,10,266,40,20,46,112,156,12,20,228,26,2,

%T 220,60,140,92,42,316,132,84,70,68,50,280,164,112,146,148,30,36,126,

%U 390,30,30,38,462,114,14,86,56,168,1600,224,104,8,72,434,142,60,750,202,318

%N Smallest k such that k*13^n is a sum of two successive primes.

%C If a(n) == 0 (mod 13), then a(n+1) = a(n)/13.

%C Records: 5, 24, 40, 266, 316, 390, 462, 1600, 2616, 5834, ..., .

%C Corresponding primes are twin primes for n = 0, 2, ..., .

%H Robert G. Wilson v, <a href="/A180137/b180137.txt">Table of n, a(n) for n = 0..200</a>

%t f[n_] := Block[{k = 1, j = 13^n/2}, While[ h = k*j; PrimeQ@h || NextPrime[h, -1] + NextPrime@h != 2 h, k++ ]; k]; Array[f, 80, 0]

%o (Python)

%o from sympy import isprime, nextprime, prevprime

%o def ok(n):

%o   if n <= 5: return n == 5

%o   return not isprime(n//2) and n == prevprime(n//2) + nextprime(n//2)

%o def a(n):

%o   k, pow13 = 1, 13**n

%o   while not ok(k*pow13): k += 1

%o   return k

%o print([a(n) for n in range(63)]) # _Michael S. Branicky_, May 04 2021

%Y Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180135, A180136, A180138.

%K nonn

%O 0,1

%A _Zak Seidov_ & _Robert G. Wilson v_, Aug 15 2010