A338255 -id:A338255 - cp's OEIS frontend

A328330 Let f(n) be the number of segments shown on a digital calculator to display n. Then a(n) is the number of terms in the sequence formed by iteration n -> f(n) until n = f(n).

3, 2, 2, 1, 1, 1, 3, 4, 2, 5, 2, 4, 4, 2, 4, 5, 2, 3, 5, 3, 4, 6, 6, 3, 6, 3, 5, 5, 3, 3, 4, 6, 6, 3, 6, 3, 5, 5, 3, 6, 2, 3, 3, 5, 3, 6, 4, 3, 6, 3, 4, 6, 6, 3, 6, 3, 5, 5, 3, 5, 5, 3, 3, 6, 3, 5, 3, 5, 5, 3, 2, 5, 5, 4, 5, 3, 2, 6, 3, 5, 3, 5, 5, 3, 5, 5, 6, 3

Offset: 1

Karl Aughton, Oct 12 2019

Type n on a calculator and count the segments on a calculator display that forms the number. Iterate until you reach a fixed point: 4, 5 or 6. a(n) is the length of the chain.

			The 12th term is 4 as 12 -> 7 -> 3 -> 5 is a chain of 4.
a(8) = 4 because 8 -> 7 -> 3 -> 5 is a chain of length 4.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A006942, A338255.

a(n) = {my(res = 0, on = n, nn = n, cn); while(nn != cn, nn = f(on); cn = on; on = nn; res++); res}
f(n) = {my(d = digits(n), x = [6, 2, 5, 5, 4, 5, 6, 3, 7, 6]); sum(i = 1, #d, x[d[i]+1])} \\ David A. Corneth, Oct 12 2019

def f(n):
    return sum((6, 2, 5, 5, 4, 5, 6, 3, 7, 6)[int(d)] for d in str(n))
def A328330(n):
    c, m = 1, f(n)
    while m != n:
        c += 1
        n, m = m, f(m)
    return c # Chai Wah Wu, Oct 27 2020

A386910 Number of iterations of seven segments count x -> A063720(x) to go from n to a fixed point.

Original entry on oeis.org

2, 2, 1, 1, 0, 0, 1, 2, 3, 1, 4, 1, 3, 3, 2, 3, 3, 1, 2, 3, 2, 3, 5, 5, 2, 5, 5, 4, 4, 5, 2, 3, 5, 5, 2, 5, 5, 4, 4, 5, 5, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 3, 5, 5, 2, 5, 5, 4, 4, 5, 2, 3, 5, 5, 2, 5, 5, 4, 4, 5, 2, 1, 4, 4, 3, 4, 4, 2, 5, 4, 4, 2, 4, 4, 2, 4, 4

Offset: 0

Marco Ripà, Aug 07 2025

A063720 is a strictly decreasing function A063720(x) < x whenever x >= 10 and all single digit x reach a fixed point A063720(x) = x with x in {4, 5}.

This sequence is unbounded and the first occurrence of a(n) = k is at n = A338255(k + 1) for any k >= 3.

			For n = 12, the a(12) = 3 steps are 12 -> 7 -> 3 -> 5 segments, and 5 is a fixed point A063720(5) = 5.

Cf. A063720, A328330, A338255, A385249.

Cf. A006942, A010371, A074458, A277116 (segments variation).

A387106 Number of iterations of seven segments count x -> A074458(x) to go from n to a fixed point.

Original entry on oeis.org

1, 2, 1, 1, 0, 0, 0, 1, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 3, 4, 2, 2, 4, 4, 2, 4, 2, 2, 3, 4, 4, 1, 2, 2, 3, 2, 4, 3, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 3, 4, 3, 3, 2, 2, 4, 2, 3, 4, 3, 2, 4, 1, 2, 2, 3, 2, 4, 3, 2, 2, 3, 2, 3, 3, 2, 3, 3

Offset: 0

Marco Ripà, Aug 16 2025

A074458 is a strictly decreasing function A063720(x) < x whenever x >= 10 and all single digit x reach a fixed point A063720(x) = x with x in {4, 5}.

This sequence is unbounded and the first occurrence of a(n) = k is at n = A338255(k + 2) for any k >= 3.

			For n = 10, the a(10) = 3 steps are 10 -> 8 -> 7 -> 4 segments, and 4 is a fixed point A074458(4) = 4.

Wikipedia, Seven-segment display.

Cf. A074458, A328330, A385249, A386910.

Cf. A006942, A010371, A063720, A277116 (segments variation).

A386244 Number of iterations of seven segments count x -> A277116(x) to go from n to a fixed point.

Original entry on oeis.org

1, 2, 1, 1, 0, 0, 0, 2, 3, 1, 4, 1, 3, 3, 1, 3, 4, 1, 2, 3, 2, 3, 5, 5, 2, 5, 2, 4, 4, 5, 2, 3, 5, 5, 2, 5, 2, 4, 4, 5, 5, 1, 2, 2, 4, 2, 5, 3, 2, 2, 2, 3, 5, 5, 2, 5, 2, 4, 4, 5, 4, 4, 2, 2, 5, 2, 4, 2, 4, 2, 2, 1, 4, 4, 3, 4, 2, 1, 5, 4, 4, 2, 4, 4, 2, 4, 4, 5, 2, 4

Offset: 0

Marco Ripà, Aug 21 2025

A277116 a strictly decreasing function A277116(x) < x whenever x >= 10 and all single digit x reach a fixed point A277116(x) = x with x in {4, 5, 6}.

This sequence is unbounded and the first occurrence of a(n) = k is at n = A338255(k + 1) for any k >= 3.

			For n = 10, the a(10) = 3 steps are 10 -> 8 -> 7 -> 3 -> 5 segments, and 5 is a fixed point A074458(5) = 5.

Wikipedia, Seven-segment display.

Cf. A277116, A328330, A385249, A386910, A387106.

Cf. A006942, A010371, A063720, A074458 (segments variation).

cp's OEIS Frontend

A328330 Let f(n) be the number of segments shown on a digital calculator to display n. Then a(n) is the number of terms in the sequence formed by iteration n -> f(n) until n = f(n).

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A386910 Number of iterations of seven segments count x -> A063720(x) to go from n to a fixed point.

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A387106 Number of iterations of seven segments count x -> A074458(x) to go from n to a fixed point.

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A386244 Number of iterations of seven segments count x -> A277116(x) to go from n to a fixed point.

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