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%I #15 May 06 2021 21:20:13
%S 5,1,4,10,2,8,12,12,36,12,28,66,30,6,18,132,36,108,34,14,48,60,12,22,
%T 150,30,6,74,54,16,8,66,150,30,6,14,374,110,22,82,62,66,108,348,114,
%U 428,190,38,570,114,102,24,82,86,178,420,84,108,328,186,126,192,76,82,24
%N Smallest k such that k*5^n is a sum of two successive primes.
%C If a(n) == 0 (mod 5), then a(n+1) = a(n)/5.
%C Records: 5, 10, 12, 36, 66, 132, 150, 374, 428, 570, 734, 840, 1938, 2036, 2220, 2968, 3132, 3444, 4014, 6090, ..., .
%C Corresponding primes are twin primes for n = 0, 1, 51, 102, 103, 202, 275, ..., .
%H Robert G. Wilson v, <a href="/A180132/b180132.txt">Table of n, a(n) for n = 0..500</a>
%t f[n_] := Block[{k = 1, j = 5^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 < 2: return [5, 1][n]
%o k, pow5 = 1, 5**n
%o while not sum2succ(k*pow5): k += 1
%o return k
%o print([a(n) for n in range(65)]) # _Michael S. Branicky_, May 01 2021
%Y Cf. A180130, A180131, A180133, 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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