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

%I A180136 #14 May 06 2021 21:21:02
%S A180136 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,
%T A180136 146,43,170,49,155,119,115,21,77,18,60,5,119,81,27,45,81,23,28,134,14,
%U A180136 262,131,86,55,7,549,81,199,107,100,184,85,80,32,43,118,299,43,224,187
%N A180136 Smallest k such that k*12^n is a sum of two successive primes.
%C A180136 If a(n) == 0 (mod 12), then a(n+1) = a(n)/12.
%C A180136 Records: 5, 18, 39, 182, 262, 549, 752, 811, 1456, ..., .
%C A180136 Corresponding primes are twin primes for n = 0, 1, 2, 5, 15, 26, 28, 55, 72, ..., .
%H A180136 Robert G. Wilson v, <a href="/A180136/b180136.txt">Table of n, a(n) for n = 0..200</a>
%t A180136 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]
%o A180136 (Python)
%o A180136 from sympy import nextprime, prevprime
%o A180136 def sum2succ(n): return n == prevprime(n//2) + nextprime(n//2)
%o A180136 def a(n):
%o A180136   if n == 0: return 5
%o A180136   k, pow12 = 1, 12**n
%o A180136   while not sum2succ(k*pow12): k += 1
%o A180136   return k
%o A180136 print([a(n) for n in range(67)]) # _Michael S. Branicky_, May 01 2021
%Y A180136 Cf. A180130, A180131, A180132, A180133, A180134, A179975, A180135, A180137, A180138.
%K A180136 nonn
%O A180136 0,1
%A A180136 _Zak Seidov_ & _Robert G. Wilson v_, Aug 15 2010