A386499 a(n) is the 5-adic valuation of A386252(n).
1, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 4, 1, 4, 6, 2, 1, 3, 3, 3, 6, 5, 3, 3, 2, 2, 6, 7, 5, 9, 7, 3, 8, 4, 8, 4, 6, 5, 6, 2, 3, 6, 4, 10, 9, 2, 4, 6, 3, 2, 3, 9, 8, 2, 6, 1, 11, 2, 5, 3, 9, 1, 1, 3, 10, 3, 3, 8, 2, 2, 7, 2, 8, 8, 5, 7, 11, 3, 5, 14
Offset: 1
Keywords
Examples
a(1) = 1 because A386252(1) = 2^1 * 3^1 * 5^1 a(2) = 1 because A386252(2) = 2^2 * 3^1 * 5^1 a(3) = 2 because A386252(3) = 2^1 * 3^1 * 5^2 a(4) = 1 because A386252(4) = 2^2 * 3^2 * 5^1
Links
- Ken Clements, Table of n, a(n) for n = 1..4000
Programs
-
Mathematica
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}] &], 5]; seq[10^12] (* Amiram Eldar, Jul 24 2025 *) -
Python
from math import log10 from gmpy2 import is_prime l2, l3, l5 = log10(2), log10(3), log10(5) upto_digits = 100 sum_limit = 3 + int((upto_digits - l3 - l5)/l2) def TP_pi_3_upto_sum(limit): # Search all partitions up to the given exponent sum. unsorted_result = [] for exponent_sum in range(3, limit+1): for i in range(1, exponent_sum -1): for j in range(1, exponent_sum - i): k = exponent_sum - i - j log_N = i*l2 + j*l3 + k*l5 if log_N <= upto_digits: N = 2**i * 3**j * 5**k if is_prime(N-1) and is_prime(N+1): unsorted_result.append((k, log_N)) sorted_result = sorted(unsorted_result, key=lambda x: x[1]) return sorted_result print([k for k, _ in TP_pi_3_upto_sum(sum_limit) ])