A356384 -id:A356384 - cp's OEIS frontend

A356386 a(n) is the number of occurrences of n in A356384.

1, 1, 2, 4, 4, 8, 0, 20, 8, 10, 6, 8, 12, 0, 48, 0, 30, 4, 30, 26, 18, 8, 4, 46, 0, 78, 0, 42, 38, 0, 36, 28, 52, 0, 60, 36, 0, 76, 24, 26, 8, 122, 0, 84, 24, 34, 42, 0, 64, 34, 86, 0, 108, 64, 40, 64, 46, 0, 98, 68, 0, 176, 20, 40, 134, 0, 42, 66, 124, 0, 114

Offset: 1

Rémy Sigrist, Aug 05 2022

Positive terms correspond to the RUNS transform of A356384.

			A356384 begins 1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 8, ...
So a(1) = 1,
   a(2) = 1,
   a(3) = 2,
   a(4) = 4,
   a(5) = 4,
   a(6) = 8,
   a(7) = 0.

Rémy Sigrist, C program

Cf. A356384.

C
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See Links section.
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A356515 For any n >= 0, let x_n(1) = n, and for any b > 1, x_n(b) is the sum of digits of x_n(b-1) in base b; x_n is eventually constant, with value a(n).

Original entry on oeis.org

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

Offset: 0

Rémy Sigrist, Aug 09 2022

This sequence is unbounded (see also A356516).

			For n = 87:
- we have:
     b    x_87(b)  x_87(b) in base b+1
     ---  -------  -------------------
       1       87            "1010111"
       2        5                 "12"
     >=3        3                  "3"
- so a(87) = 3.

Cf. A000120, A053735, A356384, A356516.

PARI
```
a(n) = { for (b=2, oo, if (n
				
```

from sympy.ntheory import digits
def a(n):
    xn, b = n, 2
    while xn >= b: xn = sum(digits(xn, b)[1:]); b += 1
    return xn
print([a(n) for n in range(105)]) # Michael S. Branicky, Aug 10 2022

a(2*n) = a(n).

cp's OEIS Frontend

A356386 a(n) is the number of occurrences of n in A356384.

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