cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

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, 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, 14, 10, 6, 7, 5, 2, 4, 2, 29, 26, 5, 15, 4, 2, 26, 15, 13, 17, 16
Offset: 1

Views

Author

Ken Clements, Jul 23 2025

Keywords

Examples

			a(1) = 1 because A386252(1) = 2^1 * 3^1 * 5^1
a(2) = 2 because A386252(2) = 2^2 * 3^1 * 5^1
a(3) = 1 because A386252(3) = 2^1 * 3^1 * 5^2
a(4) = 2 because A386252(4) = 2^2 * 3^2 * 5^1

Links

Crossrefs

Cf. A007814, A386252, A386499, A386500, A027856, A384530, A080185.

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}] &], 2]; 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((i, log_N))
    sorted_result = sorted(unsorted_result, key=lambda x: x[1])
    return sorted_result
print([i for i, _ in TP_pi_3_upto_sum(sum_limit) ])

Formula

a(n) = A007814(A386252(n)).

A386499 a(n) is the 5-adic valuation of A386252(n).

Original entry on oeis.org

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

Views

Author

Ken Clements, Jul 23 2025

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

Crossrefs

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

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) ])

Formula

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

A386500 a(n) is the 3-adic valuation of A386252(n).

Original entry on oeis.org

1, 1, 1, 2, 1, 3, 1, 4, 4, 1, 4, 1, 2, 5, 1, 3, 2, 3, 3, 2, 2, 3, 2, 3, 1, 8, 4, 7, 5, 7, 8, 3, 1, 1, 7, 3, 6, 11, 5, 1, 4, 4, 3, 1, 9, 13, 6, 3, 11, 1, 2, 11, 7, 1, 9, 15, 15, 5, 8, 12, 3, 13, 1, 14, 11, 16, 6, 19, 2, 1, 4, 8, 15, 9, 3, 10, 4, 9, 1, 8, 3, 7, 7
Offset: 1

Views

Author

Ken Clements, Jul 23 2025

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) = 1 because A386252(3) = 2^1 * 3^1 * 5^2
a(4) = 2 because A386252(4) = 2^2 * 3^2 * 5^1

Links

Crossrefs

Cf. A007949, A386252, A386498, A386499, A027856, A384530, A080185.

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}] &], 3]; 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((j, log_N))
    sorted_result = sorted(unsorted_result, key=lambda x: x[1])
    return sorted_result
print([j for j, _ in TP_pi_3_upto_sum(sum_limit) ])

Formula

a(n) = A007949(A386252(n)).
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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