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%I #11 May 06 2021 21:20:21
%S 5,2,1,1,4,12,2,1,4,3,5,8,7,34,8,11,33,26,13,9,13,90,15,40,30,5,43,9,
%T 69,38,27,79,47,9,36,6,1,92,44,51,50,16,81,21,9,50,84,14,45,59,124,
%U 215,36,6,1,20,31,35,33,46,18,3,23,114,19,41,84,14,8,35,114,19,73,14,39,68,42
%N Smallest k such that k*6^n is a sum of two successive primes.
%C If a(n) == 0 (mod 6), then a(n+1) = a(n)/6.
%C Records: 5, 12, 34, 90, 92, 124, 215, 249, 592, 601, 1099, 1282, 1406, 1589, 1700, 2688, ..., .
%C Corresponding primes are twin primes for n = 0, 1, 2, 3, 4, 7, 13, 15, 28, 69, 120, 162, 251, 257, 279 ..., .
%H Robert G. Wilson v, <a href="/A180133/b180133.txt">Table of n, a(n) for n = 0..500</a>
%t f[n_] := Block[{k = 1, j = 6^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 nextprime, prevprime
%o def sum2succ(n): return n == prevprime(n//2) + nextprime(n//2)
%o def a(n):
%o if n == 0: return 5
%o k, pow6 = 1, 6**n
%o while not sum2succ(k*pow6): k += 1
%o return k
%o print([a(n) for n in range(77)]) # _Michael S. Branicky_, May 02 2021
%Y Cf. A180130, A180131, A180132, A180134, A179975, A180135, A180136, A180137, A180138.
%K nonn
%O 0,1
%A _Zak Seidov_ & _Robert G. Wilson v_, Aug 15 2010
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