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

2,1

Comments

The sequence is well defined:

- a(2) = 3,

- for n >= 3, the expansion of n in base n-1 is "11", with sum of digits 2.

Links

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

Formula

a(n) = 2 iff n belongs to A052294.

a(n) <= n-1 for any n >= 3.

Example

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.

Prog

(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

Crossrefs

Cf. A052294, A216789, A355035 (corresponding prime numbers).

Sequence in context: A237838 A262880 A249355 * A064654 A162229 A056564

Adjacent sequences: A355031 A355032 A355033 * A355035 A355036 A355037

Keyword

nonn,base

Author

Rémy Sigrist, Jun 16 2022

Status

approved