A180135 - OEIS

%I #10 May 18 2021 19:02:16

%S 5,18,6,24,6,32,40,26,20,94,50,26,10,168,30,18,196,126,70,166,30,54,

%T 130,26,50,10,40,28,20,120,84,26,228,336,92,174,24,308,28,102,216,232,

%U 68,112,192,252,512,302,110,10,330,30,138,150,168,770,70,264,24,72,180,198

%N Smallest k such that k*11^n is a sum of two successive primes.

%C If a(n) == 0 (mod 11), then a(n+1) = a(n)/11.

%C Records: 5, 18, 24, 32, 40, 94, 168, 196, 228, 336, 512, 770, 996, 1446, 1644, 1812, 1900, 3840, ..., .

%C Corresponding primes are twin primes for n = 0, 3, ..., .

%H Robert G. Wilson v, <a href="/A180135/b180135.txt">Table of n, a(n) for n = 0..200</a>

%t f[n_] := Block[{k = 1, j = 11^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, pow11 = 1, 11**n

%o   while not ok(k*pow11): k += 1

%o   return k

%o print([a(n) for n in range(62)]) # _Michael S. Branicky_, May 18 2021

%Y Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180136, A180137, A180138.

%K base,nonn

%O 0,1

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