A382746 -id:A382746 - cp's OEIS frontend

A382744 If k appears, 5*k does not.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 63, 64, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84

Offset: 1

Jan Snellman, Apr 04 2025

nonn

Also: numbers with an even number of 5's in their prime factorization.

Natural density 5/6.

			5 is removed since 5 = 5*1, 10 is removed, 15 is removed, 20 is removed, but 25 remains.

Jan Snellman, Table of n, a(n) for n = 1..8333
Jan Snellman, Greedy Regular Convolutions, arXiv:2504.02795 [math.NT], 2025.

Cf. A003159, A007417, A382745, A382746.

select(t -> padic:-ordp(t,5)::even, [$1..100]); # Robert Israel, Apr 04 2025

Select[Range[100], EvenQ[IntegerExponent[#, 5]] &] (* Amiram Eldar, Apr 04 2025 *)

def ok(n):
    c = 0
    while n and n%5 == 0: n //= 5; c += 1
    return c&1 == 0
print([k for k in range(1, 82) if ok(k)]) # Michael S. Branicky, Apr 04 2025

from sympy import integer_log
def A382744(n):
    def f(x): return n+x-sum((k:=x//5**m)-k//5 for m in range(0,integer_log(x,5)[0]+1,2))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Apr 10 2025

[ for  in range(1,100) if (valuation(_,5) % 2) == 0]

a(n) ~ (6/5)*n.

A382745 If k appears, 7*k does not.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 85

Offset: 1

Jan Snellman, Apr 04 2025

Also numbers with an even number of 7's in their prime factorization.

Natural density 7/8.

			7 is removed since 7 = 7*1, 14, 21, 28, 35, 42 are removed, but 49 remains.

Jan Snellman, Table of n, a(n) for n = 1..8751
Jan Snellman, Greedy Regular Convolutions, arXiv:2504.02795 [math.NT], 2025.

Cf. A003159, A007417, A382744, A382746.

q:= n-> is(irem(padic[ordp](n,7), 2)=0):
select(q, [$1..85])[];  # Alois P. Heinz, Apr 04 2025

Select[Range[100], EvenQ[IntegerExponent[#, 7]] &] (* Amiram Eldar, Apr 04 2025 *)

def ok(n):
    c = 0
    while n and n%7 == 0: n //= 7; c += 1
    return c&1 == 0
print([k for k in range(1, 86) if ok(k)]) # Michael S. Branicky, Apr 04 2025

from sympy import integer_log
def A382745(n):
    def f(x): return n+x-sum((k:=x//7**m)-k//7 for m in range(0,integer_log(x,7)[0]+1,2))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Apr 10 2025

a(n) ~ (8/7)*n.

A382750 If k appears, 9*k does not.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81

Offset: 1

Jan Snellman, May 09 2025

Integers k with val(k, 9) even, where val(k, 9) is the 9-adic valuation of k.
Natural density 9/10.
Differs from A168183: 81 for example is not in A168183 but in this sequence. - R. J. Mathar, May 26 2025

			18 = 9*2 is not a term because 2 is a term.
162 = 9*18 is a term since 18 is not a term.

Jan Snellman, Table of n, a(n) for n = 1..9000
Jan Snellman, Greedy Regular Convolutions, arXiv:2504.02795 [math.NT], 2025.

Cf. A003159, A007417, A382744, A382745, A382746.

Select[Range[100], Mod[IntegerExponent[#, 3], 4] < 2 &] (* Amiram Eldar, May 12 2025 *)

from sympy import integer_log
def A382750(n):
    def f(x): return n+x-sum((k:=x//9**m)-k//9 for m in range(0,integer_log(x,9)[0]+1,2))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, May 24 2025

[ for  in range(1,100+1) if (valuation(_,3) % 4) < 2 ]

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A382744 If k appears, 5*k does not.

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A382745 If k appears, 7*k does not.

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Maple

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Python

Formula

A382750 If k appears, 9*k does not.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python

SageMath