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A386498 a(n) is the 2-adic valuation of A386252(n).

%I A386498 #13 Jul 31 2025 18:32:55
%S A386498 1,2,1,2,4,1,3,1,2,3,1,6,3,3,10,5,9,1,10,5,1,9,14,10,14,3,3,1,9,6,7,
%T A386498 15,9,7,3,1,1,3,1,17,3,13,10,16,1,4,13,11,3,5,6,8,10,15,10,3,1,3,1,9,
%U A386498 14,10,6,7,5,2,4,2,29,26,5,15,4,2,26,15,13,17,16
%N A386498 a(n) is the 2-adic valuation of A386252(n).
%H A386498 Ken Clements, <a href="/A386498/b386498.txt">Table of n, a(n) for n = 1..4000</a>
%F A386498 a(n) = A007814(A386252(n)).
%e A386498 a(1) = 1 because A386252(1) = 2^1 * 3^1 * 5^1
%e A386498 a(2) = 2 because A386252(2) = 2^2 * 3^1 * 5^1
%e A386498 a(3) = 1 because A386252(3) = 2^1 * 3^1 * 5^2
%e A386498 a(4) = 2 because A386252(4) = 2^2 * 3^2 * 5^1
%t A386498 seq[max_] := IntegerExponent[Select[Table[2^i*3^j*5^k, {i, 1, Log2[max]}, {j, 1, Log[3, max/2^i]}, {k, 1, Log[5, max/(2^i*3^j)]}] // Flatten // Sort, And @@ PrimeQ[# + {-1, 1}] &], 2]; seq[10^12] (* _Amiram Eldar_, Jul 24 2025 *)
%o A386498 (Python)
%o A386498 from math import log10
%o A386498 from gmpy2 import is_prime
%o A386498 l2, l3, l5 = log10(2), log10(3), log10(5)
%o A386498 upto_digits = 100
%o A386498 sum_limit = 3 + int((upto_digits - l3 - l5)/l2)
%o A386498 def TP_pi_3_upto_sum(limit): # Search all partitions up to the given exponent sum.
%o A386498     unsorted_result = []
%o A386498     for exponent_sum in range(3, limit+1):
%o A386498         for i in range(1, exponent_sum -1):
%o A386498              for j in range(1, exponent_sum - i):
%o A386498                 k = exponent_sum - i - j
%o A386498                 log_N = i*l2 + j*l3 + k*l5
%o A386498                 if log_N <= upto_digits:
%o A386498                     N = 2**i * 3**j * 5**k
%o A386498                     if is_prime(N-1) and is_prime(N+1):
%o A386498                         unsorted_result.append((i, log_N))
%o A386498     sorted_result = sorted(unsorted_result, key=lambda x: x[1])
%o A386498     return sorted_result
%o A386498 print([i for i, _ in TP_pi_3_upto_sum(sum_limit) ])
%Y A386498 Cf. A007814, A386252, A386499, A386500, A027856, A384530, A080185.
%K A386498 nonn
%O A386498 1,2
%A A386498 _Ken Clements_, Jul 23 2025