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

2,1

Links

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

Formula

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

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) = 2.

Prog

(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

Crossrefs

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

Sequence in context: A359227 A078178 A306396 * A105068 A363274 A120676

Adjacent sequences: A355032 A355033 A355034 * A355036 A355037 A355038

Keyword

nonn,base

Author

Rémy Sigrist, Jun 16 2022

Status

approved