%I #10 Jun 18 2022 08:41:50
%S 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,
%T 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,
%U 2,3,2,2,2,3,2,3,6,2,2,2,2,3,2,3,4,2,2
%N a(n) is the least base b >= 2 where the sum of digits of n is a prime number.
%C The sequence is well defined:
%C - a(2) = 3,
%C - for n >= 3, the expansion of n in base n-1 is "11", with sum of digits 2.
%H Rémy Sigrist, <a href="/A355034/b355034.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = 2 iff n belongs to A052294.
%F a(n) <= n-1 for any n >= 3.
%e For n = 16:
%e - we have the following expansions and sum of digits:
%e b 16_b Sum of digits in base b
%e - ------- -----------------------
%e 2 "10000" 1
%e 3 "121" 4
%e 4 "100" 1
%e 5 "31" 4
%e 6 "24" 6
%e 7 "22" 4
%e 8 "20" 2
%e - so a(16) = 8.
%o (PARI) a(n) = for (b=2, oo, if (isprime(sumdigits(n,b)), return (b)))
%o (Python)
%o from sympy import isprime
%o from sympy.ntheory.digits import digits
%o def a(n):
%o b = 2
%o while not isprime(sum(digits(n, b)[1:])): b += 1
%o return b
%o print([a(n) for n in range(2, 89)]) # _Michael S. Branicky_, Jun 16 2022
%Y Cf. A052294, A216789, A355035 (corresponding prime numbers).
%K nonn,base
%O 2,1
%A _Rémy Sigrist_, Jun 16 2022