A355035 Consider the least base b >= 2 where the sum of digits of n is a prime number; a(n) corresponds to this prime number.

2, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 3, 3, 3, 2, 2, 2, 3, 2, 3, 3, 5, 2, 3, 3, 3, 3, 3, 2, 5, 2, 2, 2, 3, 2, 3, 3, 3, 2, 3, 3, 5, 3, 3, 7, 5, 2, 3, 3, 5, 3, 7, 2, 5, 3, 3, 7, 5, 5, 5, 5, 3, 13, 2, 2, 3, 2, 3, 3, 7, 2, 3, 3, 5, 3, 7, 3, 5, 2, 3, 3, 3, 3, 3, 5, 5, 3

Offset: 2

Author

Rémy Sigrist, Jun 16 2022

Keywords

• nonn
• base

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) = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A216789, A355034 (corresponding b's).

Programs

PARI

a(n) = my (s); for (b=2, oo, if (isprime(s=sumdigits(n,b)), return (s)))

Python

from sympy import isprime
from sympy.ntheory.digits import digits
def s(n, b): return sum(digits(n, b)[1:])
def a(n):
    b = 2
    while not isprime(s(n, b)): b += 1
    return s(n, b)
print([a(n) for n in range(2, 89)]) # Michael S. Branicky, Jun 16 2022

Formula

a(n) = A216789(n, A355034(n)).