A355034 a(n) is the least base b >= 2 where the sum of digits of n is a prime number.
3, 2, 3, 2, 2, 2, 4, 2, 2, 2, 2, 2, 2, 3, 8, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 5, 2, 3, 3, 2, 4, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 4, 2, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3, 4, 2, 6, 2, 2, 3, 18, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 6, 2, 2, 2, 2, 3, 2, 3, 4, 2, 2
Offset: 2
Examples
For n = 16:
- we have the following expansions and sum of digits:
b 16_b Sum of digits in base b
- ------- -----------------------
2 "10000" 1
3 "121" 4
4 "100" 1
5 "31" 4
6 "24" 6
7 "22" 4
8 "20" 2
- so a(16) = 8.
Links
- Rémy Sigrist, Table of n, a(n) for n = 2..10000
Programs
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PARI
a(n) = for (b=2, oo, if (isprime(sumdigits(n,b)), return (b)))
-
Python
from sympy import isprime from sympy.ntheory.digits import digits def a(n): b = 2 while not isprime(sum(digits(n, b)[1:])): b += 1 return b print([a(n) for n in range(2, 89)]) # Michael S. Branicky, Jun 16 2022
Formula
a(n) = 2 iff n belongs to A052294.
a(n) <= n-1 for any n >= 3.
Comments