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%I #10 Jun 18 2022 07:43:24
%S 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,
%T 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,
%U 3,7,2,3,3,5,3,7,3,5,2,3,3,3,3,3,5,5,3
%N Consider the least base b >= 2 where the sum of digits of n is a prime number; a(n) corresponds to this prime number.
%H Rémy Sigrist, <a href="/A355035/b355035.txt">Table of n, a(n) for n = 2..10000</a>
%F a(n) = A216789(n, A355034(n)).
%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) = 2.
%o (PARI) a(n) = my (s); for (b=2, oo, if (isprime(s=sumdigits(n,b)), return (s)))
%o (Python)
%o from sympy import isprime
%o from sympy.ntheory.digits import digits
%o def s(n, b): return sum(digits(n, b)[1:])
%o def a(n):
%o b = 2
%o while not isprime(s(n, b)): b += 1
%o return s(n, b)
%o print([a(n) for n in range(2, 89)]) # _Michael S. Branicky_, Jun 16 2022
%Y Cf. A216789, A355034 (corresponding b's).
%K nonn,base
%O 2,1
%A _Rémy Sigrist_, Jun 16 2022