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

1,3

Links

Ken Clements, Table of n, a(n) for n = 1..4000

Formula

a(n) = A112765(A386252(n)).

Example

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

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 *)

Prog

(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) ])

Crossrefs

Cf. A112765, A386252, A386498, A386500, A027856, A384530, A080185.

Sequence in context: A236548 A249949 A373246 * A155798 A055652 A290084

Adjacent sequences: A386496 A386497 A386498 * A386500 A386501 A386502

Keyword

nonn

Author

Ken Clements, Jul 23 2025

Status

approved